Adams, W.W., Boyle, A., Loustaunau, P., Transitivity for Weak and Strong Gröbner Bases, J. Symb. Comp. 15 (1993), 49–65.Google Scholar

Alonso, M. E., Castro-Jimènez, F. J., Hauser, H., Encoding Algebraic Power Series arxiv.ong/pdf/1403.4104v1.pdf

Alonso, M. E., Luengo, I., Raimondo, M., An Algorithm on Quasi-Ordinary Polynomials, L. N. Comp. Sci. 357 (1989), 59–73, Springer.Google Scholar

Anick, D. J., On the Homology of Associative Algebras, Trans. A.M.S. 296 (1986), 641–659.Google Scholar

Apel, J., Gröbnerbasen in Nichetkommutativen Algebren und ihre Anwendung, Dissertation, Leipzig (1988).

Apel, J., Division of Entire Functions by Polynomial Ideals, L. N. Comp. Sci. 948 (1995), 82–958, Springer.Google Scholar

Apel, J., The Theory of Involuting Divisions and an Application to Hilbert Function Computations, J. Symb. Comp. 25 (1998), 683–704.Google Scholar

Apel, J., Computational Ideal Theory in Finitely Generated Extension Rings, T.C.S. 224 (2000), 1–33.Google Scholar

Apel, J., Lassner, W., An algorithm for calculations in enveloping fields of Lie algebras, In: Proc. Int. Conf. on Comp. Algebra and Its Appl. in Theoretical Physics, JINR D11-85-792, Dubna (1985), 231–241.

Apel, J., Lassner, W., Computation and Simplification in Lie Fields, L. N. Comp. Sci. 378 (1987), 468–478, SpringerGoogle Scholar

Apel, J., Stückrad, J., Tworzewski, P., Winiarski, T., Reduction of Everywhere Convergent Power Series with Respect to Gröbner Bases, J. Pure Appl. Algebra 110 (1996), 113–129.Google Scholar

Apel, J., Stückrad, J., Tworzewski, P., Winiarski, T., Properties of Entire Functions over Polynomial Rings via Gröbner Bases, J. AAECC 14 (2003), 1–10.Google Scholar

Artin, M., Schelter, W., Graded Algebras of Global Dimension 3, Adv. Math. 66 (1987), 171–216.Google Scholar

Aschenbrenner, M., Hillar, C. J.Finite Generation of Symmetric Ideals, Trans. A.M.S. 359 (2007), 5171–5192, and Trans. A.M.S. 361 (2009), 5627.Google Scholar

Aschenbrenner, M., Hillar, C. J.An Algorithm for Finding Symmetric Gröbner Bases in Infinite Dimensional Ring, Proc. ISSAC'08 (2008), 117–123, ACM.Google Scholar

Assi, A., Standard Bases, Criticals Tropisms and Flatness, J. AAECC 4 (1993), 197–215.Google Scholar

Bächler, T., Gerdt, V., Lange-Hegermann, M., Robertz, D., Thomas Decomposition of Algebraic and Differentil Systems, J. Symb. Comp. 47 (2012), 1223–1266.Google Scholar

Bardet, M., Étude des systèmes algébriques sutdterminés. Applications aux codes correcteures et à la cryptographie, These de Doctorat, Paris6 (2004).

Barkee, B., Gröbner Bases. The Ancient Secret Mystic Power of the Algu Compubraicus. A Revelation Whose Simplicity Will Make Ladies Swoon and Grown Men Cry, Cornell University MSI Technical Report (1988).

Bayer, D., The Division Algorithm and the Hilbert Scheme, PhD Thesis, Harvard (1981).

Becker, T., Standard Bases and Some Computations in Rings of Power Series, J. Symb. Comp. 10 (1990), 165–178.Google Scholar

Becker, T., Standard Bases in Power Series Rings: Uniqueness and Superfluous Criterial Pairs, J. Symb. Comp. 15 (1993), 251–265.Google Scholar

Becker, T., Weispfenning, V., Gröbner Bases, Springer (1982).

Bergman, G. H., The Diamond Lemma for Ring Theory, Adv. Math. 29 (1978), 178–218.Google Scholar

Bigatti, A., Aspetti combinatorici e computazionali dell'Algebra Commutative, PhD Thesis, Genova (1995).

Bigatti, A., Upper Bounds for the Betti Numbers of a Given Hilbert Function, Communications in Algebra 21 (1993), 2317–2334.Google Scholar

Borges, M. A., Borges, M., Gröbner Bases Property on Elimination Ideal in the Noncommutative Case. In: Buchberger, B., Winkler, F. (Eds.), Gröbner Bases and Application (1998), Cambridge University Press, 323–337.

Borges, M. A., Borges, M., Castellanos, J.A., Martinez, E., The Symmetric Groups Given by a Gröbner Basis, J. Pure Appl. Algebra 207 (2006), 149–154.Google Scholar

Borges, M. A., Estrada, M. V., Gröbner Bases and G-presentations of Finite Generated Monoids (1995), preprint.

Borodin, A., On Relating Time and Space to Size and Depth, SIAM Journal on Computing 6 (1977), 733.Google Scholar

Borodin, A., Cook, S., Pippenger, N.Parallel Computation for Well-endowed Rings and Space-bounded Probabilistic Machines, Information and Control 58 (1983), 113–136.Google Scholar

Bouillet, F., Lazard, D., Ollivier, F., Petitot, M., Representation for the Radical of a Finitely Generated Differential Ideal (1996), Proc. ISSAC'95 (1995), 158–166, ACM.

Buchberger, B.Miscellaneous Results on Gröbner Bases for Polynomial Ideals II. Technical Report 83/1, University of Delaware, Department of Computer and Information Sciences, 1983. p. 31.

Bueso, J.L., Castro, F. J., Gomez Torrecilla, J., Lobillo, F. J., An Introduction to Effective Calculus in Quantum Groups. In : Caenepeel, S., Verschoren, A. (Eds.) Rings, Hopf Algebras and Brauer Groups, M. Decker (1998), 55–83.

Cartan, E., Sur l'intégration des systèmes d’équations aux différentielles totals, Ann. Éc. Norm. 3e série 18 (1901), 241.Google Scholar

Cartan, E., Sur la structure des groupes infinis de transformations, Ann. Éc. Norm. 3e série 21 (1904), 153.Google Scholar

Cartan, E., Sur les systèmes en involution d’équations aux dérivées partielles du second ordre à une fonction inconnue de trois variables indépendentes, Bull. Soc. Math. 39 (1920), 356.Google Scholar

Ceria, M., Roggero, M., Term-ordering Free Involutive Bases, J. Symb. Comp. 68 (2015), 87–108. http://arxiv.org/pdf/1310.0916v1.pdfGoogle Scholar

Chyzak, F., Salvy, B., Non-commutative Elimination in Ore Algebras Proves Multivariate Identities, J. Symb. Comp. 26 (1998), 187–227.Google Scholar

Cioffi, F., Roggero, M., Flat Families by Strongly Stable Ideals and a Generalization of Gröbner Bases, J. Symb. Comp. 46 (2011), 1070–1084.Google Scholar

Cohn, P. M., Noncommutative Unique Factorization Domains, Trans. A.M.S. 109 (1963), 313–331.Google Scholar

Cohn, P. M., Ring with a Weak Algorithm, Trans. A.M.S. 109 (1963), 332–356.Google Scholar

Cojocaru, S., Ufnarovski, V., Noncommutative Gröbner Basis, Hilbert Series, Anick's Resolution and BERGMAN under MS-DOS, Computer Science Journal of Moldova 3 (1995), 24–39.Google Scholar

Deery, T., Rev-lex Segment Ideals and Minimal Betti Numbers, Queens Papers in Pure and Applied Algebra, The Curves Seminar, vol. X (1999).

de Graaf, W. A., Wisliceny, J., Constructing Bases of Finitely Presented Lie Algebras using Gröbner Bases in Free Algebras, Proc. ISSAC'99 (1999), 37–44, ACM.

Delassus, E., Extension du théorème de Cauchy aux systèmes les plus généraux d’équations aux dérivées partielles, Ann. Éc. Norm. 3e série 13 (1896), 421–467.Google Scholar

Delassus, E., Sur les systèmes algébriques et leurs relations avec certains systèmes d'equations aux dérivées partielles, Ann. Éc. Norm. 3e série 14 (1897), 21–44.Google Scholar

Delassus, E., Sur les invariants des systèmes différentiels, Ann. Éc. Norm. 3e série 25 (1908), 255–318.Google Scholar

Drach, J., Essai sur la théorie général de l'integration et sur la classification des Trascendentes, Ann. Éc. Norm. 3e série 15 (1898), 245–384.Google Scholar

Dubé, T.W., The Structure of Polynomial Ideals and Gröbner Bases. SIAM J. Comput., 19(4) (2006), 750–773.Google Scholar

Eder, C., Perry, J., F5C: A Variant of Faugère's F5 Algorithm with Reduced Gröbner Bases, J. Symb. Comp. 45 (2010), 1442–1450.Google Scholar

Eder, C., Perry, J., Signature-based Algorithms to Compute Gröbner Bases, Proc. ISSAC'11 (2011), 99–106, ACM.

Eisenbud, D., Peeva, I., Sturmfels, B., Non-commutative Gröbner Bases for Commutative Algebras, Proc. A.M.S. 126 (1998) 687–691.Google Scholar

Farkas, D. R., Feustel, C. D., Green, E. L.Synergy in the Theories of Gröbner Bases and Path Algebras, Can. J. Math. 45 (1993), 727–739.Google Scholar

Faugère, J.-C., A New Efficient Algorithm for Computating Gröbner Bases (F4), J. Pure Appl. Algebra 139 (1999), 61–88.Google Scholar

Faugère, J.-C., A New Efficient Algorithm for Computating Gröbner Bases without Reduction to Zero (F5), Proc. ISSAC 2002 (2002), 75–83, ACM.Google Scholar

Galligo, A., Some Algorithmic Questions on Ideals of Differential Operators, L. N. Comp. Sci. 204 (1985), 413–421, Springer.Google Scholar

Gateva-Ivanova, T., Noetherian Properties and Growth of Some Associative Algebras, Progress in Mathematics 94 (1990), 143–158, Birkhäuser.Google Scholar

Gateva-Ivanova, T., On the Noetherianity of Some Associative Finitely Presented Algebras, J. Algebra 138 (1991), 13–35.Google Scholar

Gateva-Ivanova, T., Noetherian Properties of Skew Polynomial Rings with Binomial Relations, Trans. A.M.S. 345 (1994), 203–219.Google Scholar

Gateva-Ivanova, T., Skew Polynomial Rings with Binomial Relations, J. Algebra 185 (1996), 710–753.Google Scholar

Giesbrecht, M., Reid, G., Zhan, Y., Non-Commutative Grobner Bases in Poincare–Birkhoff–Witt Extension, The Ontario Research Centre for Computer Algebra, ORCCA Technical Report TR-03-02 (2003)

Gerdt, V. P., Involutive algorithms for computing Gröbner bases. In Computational Commutative and Non-Commutative Algebraic Geometry, Cojocaru, S., Pfister, G., Ufnarovski, V. (Eds.), NATO Science Series, IOS Press, 2005, pp. 199–225.

Gerdt, V. P., Blinkov, Y. A., Involutive Bases of Polynomial Ideals, Math. Comp. Simul. 45 (1998), 543–560.Google Scholar

Gerdt, V. P., Blinkov, Y. A., Minimal Involutive Bases, Math. Comp. Simul. 45 (1998), 519–541.Google Scholar

Gerdt, V. P., Blinkov, Y. A., Involutive Division Generated by an Antigraded Monomial Ordering, L. N. Comp. Sci. 6885 (2011), 158–174, Springer.Google Scholar

Gerdt, V. P., Yanovich, D.A., Effectiveness of Involutive Criteria in Computation of Polynomial Janet Bases, Programming and Computer Software 32 (2006), 134–138.Google Scholar

Gerdt, V. P., Zinin, M.V., A Pommaret Division Algorithm for Computing Gröbner Bases in Boolean Rings. Proceedings of ISSAC 2008, 95–102, ACM Press.

Gerritzen, L., On Non-Associative Gröbner Bases, Symposium in Honor of Bruno Buchberger's 60th Birthday, RISC-Linz, 2002.

Gerritzen, L., Tree Polynomials and Non-Associative Gröbner Bases, J. Symb. Comp. 41 (2006), 297–316.Google Scholar

Green, E. L., Multiplicative Bases, Gröbner Bases and Right Gröbner Bases, J. Symb. Comp. 29 (2000), 601–624.Google Scholar

Göbel, M., Computing Bases for Rings of Permutation-invariant Polynomials, J. Symb. Comp. 19 (1995), 258–291.Google Scholar

Göbel, M., Symedeal Gröbner Bases, L. N. Comp. Sci. 1103 (1996), 48–62, Springer.Google Scholar

Göbel, M., A Constructive Description of SAGBI Bases for Polynomial Invariants of Permutation Groups, J. Symb. Comp. 26 (1998), 261–272.Google Scholar

Göbel, M., On the Reduction of G-invariant Polynomials for Arbitrary Permutation Groups, Progress in Computer Science and Applied Logic 15 (1998), 35–46.Google Scholar

Göbel, M., The ‘Smallest’ Ring of Polynomial Invariants of a Permutation Group which has no Finite SAGBI Bases with Respect to any Admissible Order, Theoret. Comput. Sci. 222 (1999), 177–187.Google Scholar

Göbel, M., Rings of Polynomial Invariants of the Alternating Group Have No Finite SAGBI Bases with Respect to any Admissible Order, Information Processing Letters. 74 (2000), 15–18.CrossRefGoogle Scholar

Göbel, M., Finite SAGBI Bases for Polynomial Invariants of Conjugates of Alternating Groups, Mathematics of Computation 71 (2001), 761–765.Google Scholar

Göbel, M., Kredel, H., Reduction of Permutation-Invariant Polynomials. A Noncommutative Case Study, Information and Computation 175 (2002), 158–170.Google Scholar

Gräbe, H.-G., The Tangent Cone Algorithm and Homogeneization, J. Pure Appl. Algebra 97 (1994), 303–312.Google Scholar

Gräbe, H.-G., Algorithms in Local Algebra, J. Symb. Comp. 19 (1995), 545–557.Google Scholar

Gräbe, H.-G., Triangular Systems and Factorized Gröbner Bases, L. N. Comp. Sci. 948 (1995), 248–261, Springer.Google Scholar

Gräbe, H.-G., Minimal Primary Decomposition and Factoring Gröbner Bases, J. AAECC 8 (1997), 265–278.Google Scholar

Granger, M., Oaku, T., Takayama, N., Tangent Cone Algorithm for Homogenized Differential Operations, J. Symb. Comp. 39 (2005), 417–431.Google Scholar

Grassmann, H., Greuel, G.-M., Martin, B., et al., Standard Bases, Syzygies and their Implementation in SINGULAR, University of Kaiserslautern Fach. Math. Preprint 251 (1994).Google Scholar

Greuel, G.-M., Pfister, G., Advances and Improvements in the Theory of Standard Bases and Syzygies, Arch. Math. 66 (1996), 131–176.Google Scholar

Greuel, G.-M., Seelisch, F., Wienand, O., The Gröbner Basis of the Ideal of Vanishing Polynomials, J. Symb. Comp. 46 (2011), 561–570.Google Scholar

Gunther, N., Sur une inègalité dans la théorie des fonctions rationnelles et entieres (in Russian) [Journal de l'Institut des Ponts et Chaussées de Russie] Izdanie Inst. In?z. Putej Soob?s?cenija Imp. Al. I. 84 (1913).Google Scholar

Gunther, N., Sur la forme canonique des systèmes déquations homogènes (in Russian) [Journal de l'Institut des Ponts et Chaussées de Russie] Izdanie Inst. In?z. Putej Soob?s?cenija Imp. Al. I. 84 (1913).Google Scholar

Gunther, N., Sur les caractéristiques des systémes d’équations aux dérivées partialles, C. R. Acad. Sci. Paris 156 (1913), 1147–1150.Google Scholar

Gunther, N., Sur la forme canonique des equations algébriques, C. R. Acad. Sci. Paris 157 (1913), 577–80.Google Scholar

Gunther, N., Sur la théorie générale des systèmes d’équations aux dérivées partielles, C. R. Acad. Sci. Paris 158 (1914), 853–856, 1108–1111.Google Scholar

Gunther, N., Sur l'extension du théorème de Cauchy aux systèmes d’équations aux dérivées partielles (in Russian), Mat. Sbornik 32 (1924) 367–434.Google Scholar

Gunther, N., Sur les modules des formes algébriques, Trudy Tbilis. Mat. Inst. 9 (1941), 97–206.Google Scholar

Hartley, D., Tuckey, P., A Direct Characterization of Gröbner Bases in Clifford and Grassmann Algebras, J. Symb. Comp. 20 (1995), 197–205.Google Scholar

Hartshorne, R., Connectedness of the Hilbert Scheme, Publ. Math. I.H.E.S. 29 (1966), 261–304.Google Scholar

Hashemi, A., Ars, G., Extended F5 criteria, Adv. Math. 66 (1987), 171–216.Google Scholar

Hermiller, S. M., Kramer, X. H., Laubenbacher, R.C.Monomial Orderings, Rewriting Systems and Gröbner Bases for the Commutator Ideal of a Free Algebra, J. Symb. Comp. 27 (1999), 133–141.Google Scholar

Hermiller, S. M., McCammond, J., Noncommutative Gröbner Bases for the Commutator Ideal, Int. J. Algebra Comp. 16 (2006) 187–202.CrossRefGoogle Scholar

Heyworth, A., One-sided Noncommutative Gröbner Bases with Applications to Computing Green's Relations, J. Algebra 242 (2001) 401–416.CrossRefGoogle Scholar

Hironaka, H., Idealistic Exponents of Singularity. In: Algebraic Geometry, The Johns Hopkins Centennial Lectures (1977), 52–125.Google Scholar

Hulett, H., Maximum Betti Numbers of Homogeneous Ideals with a Given Hilbert Function, Communications in Algebra 21 (1993), 2335–2350.Google Scholar

Hulett, H., Maximum Betti Numbers for a Given Hilbert Function, PhD Thesis, Urbana- Champaign (1993).

Janet, M., Sur les systèmes d’équations aux dérivées partielles, J. Math. Pure et Appl. 3 (1920), 65–151.Google Scholar

Janet, M., Les modules de formes algébraiques et la théorie générale des systèmes diffèrentielles, Ann. Éc. Norm. 3e série 41 (1924), 27–65.Google Scholar

Janet, M., Les systèmes d’équations aux dérivées partielles, Mémorial Sci. Math. XXI (1927), Gauthiers-Villars.Google Scholar

Janet, M., Leçons sur les systèmes d’équations aux dérivées partielles (1929), Gauthiers-Villars.

Kandri-Rody, A., Kapur, D., Computing the Gröbner Basis of an Ideal in Polynomail Rings over the Integers. In: Proc. Third MACSYMA Users’ Conference (1984).

Kandri-Rody, A., Kapur, D., Computing the Gröbner Basis of an Ideal in Polynomail Rings over a Euclidean Ring, J. Symb. Comp. 6 (1990), 37–56.Google Scholar

Kandri-Rody, A., Weispfenning, W., Non-commutative Gröbner Bases in Algebras of Solvable Type, J. Symb. Comp. 9 (1990), 1–26.Google Scholar

Kapur, D., Madlener, K., A Completion Procedure for Computing a Canonical Basis for a k-subalgebra. In: Kaltofen, E., Watt, S. M. (Eds.), Computer and Mathematics, Springer (1989), 1–11.

Kapur, D., Sun, Y., Wang, D., A New Algorithm for Computing Comprehensive Gröbner Systems, Proc. ISSAC 2010 (2010), 29–36, ACM.

Keller, B. J., Alternatives in Implementing Noncommutative Gröbner Basis Systems, Progress in Computer Science and Applied Logic 15 (1991), 105–126, Birkhäuser.Google Scholar

Kobayashi, Y., A Finitely Presented Monid which has Solvable Word Problem but has no Regular Complete Presentation, Theoret. Comput. Sci. 146 (1995), 312–329.Google Scholar

Kredel, H., Solvable Polynomial Rings, Dissertation, Passau (1992).

Kruskal, J. B., The Theory of Well-quasi-ordering: A Frequently Discovered Concept, J. Combin. Theory Ser. A 13 (1972) 297–305.CrossRefGoogle Scholar

Kühnle, K., Mayr, E.W., Exponential Space Computation of Gröbner Bases, Proc. ISSAC 96 (1996) 63–71, ACM.

Labontè, G., An Algorithm for the Construction of Matrix Representations for Finite Present Non-commutative Algebras, J. Symb. Comp. 9 (1990), 27–38.Google Scholar

Lambek, J., Lectures on Rings and Modules, Blaisdell (1966).

LaScala, R., Gröbner Bases and Gradings for Partial Difference Ideals, Math. Comp. 84 (2015), 959–985. arxiv.ong/pdf/1112.2065v4.pdfGoogle Scholar

LaScala, R., Levandovskyy, V., Letterplace Ideals and Non-commutative Gröbner Bases, J. Symb. Comp. 44 (2009), 1374–1393.Google Scholar

LaScala, R., Levandovskyy, V., Skew Polynomial Rings, Gröbner Bases and the Letterplace Embedding of the Free Associative Algebra, J. Symb. Comp. 48 (2013), 110–131.Google Scholar

Lascoux, A., Pragacz, P.S-function Series, J. Phys.A Math. Gen. 21 (1988), 4105– 4114.Google Scholar

Lauer, M., Canonical Representative for Residue Classes of a Polynomial Ideal, Proc. 1976 SymSAC, (1976) 339–345, ACM.

Lazard, D., Solving Zero-dimensional Algebraic Systems, J. Symb. Comp. 15 (1992), 117–132.Google Scholar

Lella, P., A Network of Rational Curves on the Hilbert Scheme, arxiv.ong/pdf/1006.5020v2.pdf

Levandovskyy, V. L., Non-commutative Computer Algebra for Polynomiakl Algebras: Gröbner Bases, Applications and ImplementationDissertation, Kaiserslautern (2005).

Levandovskyy, V. L., Studzinski, G., Schnitzler, B., Enhanced Computations of Gröbner Bases in Free Algebras as a New Application of the Letterplace ParadigmProc. ISSAC'13 (2013), 259–266, ACM.

Levin, A. B., Gröbner Bases with Respect to Several Orderings and Multivariate Dimension Polynomials, J. Symb. Comp. 42 (2007), 561–578.Google Scholar

Li, H., Looking for Gröbner Basis Theory for (Almost) Skew 2-nomial Algebras, J. Symb. Comp. 45 (2010), 918–942.Google Scholar

Liu, J., The Membership Problem for Ideals of Binomial Skew Polynomial Rings, Proc. ISSAC 2001 (2001), 192–194, ACM

Macaulay, F. S., Some Formulae in Elimination, Proc. London Math. Soc. (1) 35 (1903), 3–27.Google Scholar

Macaulay, F. S., The Algebraic Theory of Modular Systems, Cambridge University Press (1916).

Macaulay, F. S., Some Properties of Enumeration in the Theory of Modular Systems, Proc. London Math. Soc. 26 (1927), 531–555.Google Scholar

MacMillan, W. D., A Reduction of a Systems of Powers Series to an Equivalent System of Polynomials, Math. Ann. 72 (1912) 157–179.Google Scholar

MacMillan, W. D., A Method for Determining the Solutions of a System of Analytic Functions in the Neighborhood of a Branch Point, Math. Ann. 72 (1912), 180–202.Google Scholar

Madlener, K., Reinert, B., String Rewriting and Gröbner Bases – A General Approach to Monoid and Group Rings, Progr. Comp. Sci. Appl. Logic 15 (1991), 127–180, Birkhäuser.Google Scholar

Madlener, K., Reinert, B., Computing Gröbner Bases in Monoid and Group Rings, Proc.ISSAC '93 (1993), 254–263, ACM.Google Scholar

Mall, D., Characterizations of Lexicographical Sets and Simply-connected Hilbert Schemes, L. N. Comp. Sci. 1252 (1997), 221–236, Springer.Google Scholar

Mall, D., On the Relation between Gröbner and Pommaret Bases, J. AAECC 9 (1998), 117–124.Google Scholar

Mansfield, E. L., Szanto, A., Elimination Theory for Differential Difference Polynomials, Proc. ISSAC 2002 (2002), 191–198, ACM.

Månsson, J., A Prediction Algorithm for Rational Language, Licentiate Thesis, Lund University (2001).

Månsson, J., Nordbeck, B., Regular Gröbner Bases, J. Symb. Comp. 33 (2002), 163–181.Google Scholar

Marinari, M.G., Sugli ideali di Borel, Boll. UMI 4 (2001), 207–237.Google Scholar

Marinari, M.G., Ramella, L., Some Properties of Borel Ideals, J. Pure Appl. Algebra 139 (1999), 833–200.Google Scholar

Marinari, M.G., Ramella, L., A Characterization of Stable and Borel IdealsJ. AAECC 16 (2005), 45–68.Google Scholar

Marinari, M.G., Ramella, L., Borel Ideals in Three Variables, Beiträge zur Algebra und Geometrie 47 (2006), 195–209.Google Scholar

Markwig, T., Standard Bases in K[[t1, …, tm]][x1, …, xn]s, J. Symb. Comp. 43 (2008), 765–786.Google Scholar

Mårtensson, K., An Algorithm to Detect Regular Behaviour of Binomial Gröbner Basis Rational Language, Master's Thesis, Lund University (2006).

Maurer, J., Puiseux Expansions for Space Curves, Manuscripta Math., 32 (1980), 91–100.Google Scholar

Mayr, E.W., Ritscher, S., Dimension-dependent Bounds for Gröbner Bases of Polynomial Ideals, J. Symb. Comp. 49 (2013), 78–94.Google Scholar

Mayr, E.W., Ritscher, S., Space-efficient Bounds for Gröbner Bases of Polynomial Ideals, Proc. ISSAC 2011 (2011).

Maurer, J., Puiseux Expansions for Space Curves, Manuscripta Math., 32 (1980), 91–100.CrossRefGoogle Scholar

Miller, J. L., Analogs of Gröbner Bases in Polynomial Rings over a Ring, J. Symb. Comp. 21 (1996), 139–153.Google Scholar

Miller, J. L., Effective Algorithms for Intrisic Computing SAGBI-Gröbner Base in Polynomial Rings over a Ring. In Buchberger, B., Winkler, F. (Eds.), Gröbner Bases and Application (1998) 421–433, Cambridge University Press.

Möller, H. M., On the Construction of Gröbner Bases Using Syzygies, J. Symb. Comp. 6 (1988), 345–359.Google Scholar

Montes, A., A New Algorithm for Discussing Gröbner Bases with Parameters, J. Symb. Comp. 33 (2002), 183–208.Google Scholar

Montes, A., Using Kapur–Sun–Wang Algorithm for the Gröbner Cover, Proc. EACA 2012 (2012), 135–138, Universidad de Alcalá de Henares.

Montes, A., Wibmer, M., Gröbner Bases for Polynomial Systems with Parameters, J. Symb. Comp. 45 (2010), 1391–1425.Google Scholar

Mosteig, E., Sweedler, M., Valuations and Filtrations, J. Symb. Comp. 34 (2002), 399–435.Google Scholar

Nabeshima, K., A Speed-up of the Algorithm for Computing Comprehensive Gröbner Systems, Proc. ISSAC'2007 (2007), 299–306. ACM.

Nordbeck, P., On Some Basic Applications of Gröbner Bases in Non-commutative Polynomial Rings. In: Buchberger, B., Winkler, F. (Eds.), Gröbner Bases and Application (1998) Cambridge University Press, 463–472.

Nordbeck, P., Canonical Subalgebra Bases in Non-commutative Polynomial Rings, Proc. ISSAC'98 (1998), 140–146, ACM.

Nordbeck, P., Canonical Bases for Subalgebras of Factor Algebras, Computer Science Journal of Moldavia 7 (1999), 63–79, ACM.

Norton, G. H., Sălăgean, A., Strong Gröbner Bases for Polynomials Over a Principal Ideal Ring, Bull. Austral. Math. Soc. 64 (2001), 505–528.Google Scholar

Norton, G. H., Sălăgean, A., Gröbner Bases and Products of Coefficient Rings, Bull. Austral. Math. Soc. 65 (2002), 147–154.Google Scholar

Norton, G. H., Sălăgean, A., Cyclic Codes and Minimal Strong Gröbner Bases Over a Principal Ideal Ring, Finite Fields and Their Applications 9 (2003), 237–249.Google Scholar

Ollivier, F., Canonical Bases: Relations with Standard Bases, Finiteness Conditions and Application to Tame Automorphisms, Progr. Math. 94 (1990), 379–400, Birkhäuser.Google Scholar

Ore, O., Linear Equations in Non-commutative Fields, Ann. Math. 32 (1931), 463–477.Google Scholar

Ore, O., Theory of Non-commutative Polynomials, Ann. Math. 34 (1933), 480–508.Google Scholar

Pan, L., On the D-bases of Polynomial Ideals Over Principal Ideal Domains, J. Symb. Comp. 7 (1988), 55–69.Google Scholar

Pauer, F., Gröbner Bases with Coefficients in Rings, J. Symb. Comp. 42 (2007), 1003–1011.Google Scholar

Pesch, M., Gröbner Bases in Skew Polynomial RingsDissertation, Passau (1997).

Pesch, M., Two-sided Gröbner Bases in Iterated Ore Extensions, Progr. Computer Sci. Appl. Logic 15 (1991), 225–243, Birkhäuser.Google Scholar

Pommaret, J. F., Systems of Partial Differential Equations and Lie Pseudogroups, Gordon and Brach (1978).

Pommaret, J. F., Haddak, A.Effective Methods for Systems of Algebraic Partial Differential Equations, Prog. Math. 94 (1990), 411–426, Birkhäuser.Google Scholar

Pfister, G., The Tangent Cone Algorithm and Some Applications to Local Algebraic Geometry, Progr. Math. 94 (1990), 401–410, Birkhäuser.Google Scholar

Pfister, G., Schönemann, H., Singularities with Exact Poincaré Complex but not Quasihomogeneous, Rev. Mat. Univ. Complutense Madrid 2 (1989), 161–174.Google Scholar

Pritchard, F. L., A Syzygies Approach to Non-commutative Gröbner Bases, Preprint (1994).

Pritchard, F. L., The Ideal Membership Problem in Non-commutative Polynomial Rings, J. Symb. Comp. 22 (1996), 27–48.Google Scholar

Rajee, S., Non-associative Gröbner Bases, J. Symb. Comp. v (2006), 887–904.Google Scholar

Renschuch, B., Roloff, H., Rasputin, G. G. et. al., Beiträge zur konstructiven Theorie des Polynomideal XXIII: Vergessene Arbeiten des Leningrader Mathematikers N.M. Gjunter on Polynomial Ideals, Wiss. Z. Pädagogische Hochschule Karl Liebknecht, Postdam, 31 (1987) 111–126. English translation (by M. Abramson) in ACM SIGSAM Bull. 37 (2003) 35–48.

Reichstein, Z., SAGBI Bases in Rings of Multiplicative Invariants, Comment. Math. Helv. 78, 185–202.

Reinert, B., On Gröbner Basis in Monoids and Group Rings, Dissertation, Kaiserslautern (1995).

Reinert, B., A Systematic Study of Gröbner Basis Methods, Habilitation, Kaiserslautern (2003).

Reinert, B., Gröbner Bases in Function Ring – A Guide for Introducing Reduction Relations to Algebraic Structures, J. Symb. Comp. 41 (2006), 1264–1294.Google Scholar

Richman, F., Constructive Aspects of Noetherian Rings, Proc. AMS 44 (1974), 436–441.Google Scholar

Riquier, C., De l'existence des intégrales dans un système differentiel quelconque, Ann. Éc. Norm. 3e série 10 (1893) 65–86.CrossRefGoogle Scholar

Riquier, C., Sur une questione fondamentale du Calcul intégral, Acta Mathematica 23 (1899), 203.Google Scholar

Riquier, C., Les systèmes d’équations aux dérivées partielles (1910), Gauthiers-Villars.

Riordan, J., Combinatorial Identities (1968), Wiley.

Ritt, J. F., Prime and Composite Polynomials. Trans. A.M.S. 23 (1922), 51–66.Google Scholar

Ritt, J. F., Differential Equations from the Algebraic Standpoint, A.M.S. Colloquium Publications 14 (1932).Google Scholar

Ritt, J. F., Differential Algebra, A.M.S. Colloquium Publications 33 (1950).Google Scholar

Robbiano, L., Sweedler, M., Subalgebra Bases, L. Math. 1430 (1988), 61–87, Springer.Google Scholar

Robinson, L. B., Sur les systémes d’équations aux dérivées partialles, C. R. Acad. Sci. Paris 157 (1913), 106–108.Google Scholar

Robinson, L. B.A new Canonical Form for Systems of Partial Differential Equations, Amer. J. Math. 39 (1917), 95–112.Google Scholar

Rosenmann, A., An Algorithm for Constructing Gröbner and Free Schreier Bases in Free Group Algebras, J. Symb. Comp. 16 (1993), 523–549.Google Scholar

Saito, T., Iwamoto, T., Kobayasli, Y., Kajitori, K., Strongly Compatible Total Orders on Free Monoids, Semigroup Forum 43 (1991), 357–366.Google Scholar

Saito, T., Katsura, M., Kobayasli, Y., Kajitori, K., On Totally Ordered Free Monoids. In: Words, Language and Combinatorics, World Scientific (1992), 454–479.

Salomaa, A., Jewels of Formal Language Theory, Pitmann (1981).

Saracino, D., Weispfenning, V., On Algebraic Curves Over Commutative Regular Rings, L. Math. 498 (1975), 307–383, Springer.Google Scholar

Sato, Y., Suzuki, A., Discrete Comprehensive Gröbner Bases, Proc. ISSAC 2001 (2001), 292– 296, ACM.

Sato, Y., Suzuki, A., An Alternative Approach to Comprehensive Gröbner Bases, J. Symb. Comp. 36 (2003), 649–667.Google Scholar

Sato, Y., Suzuki, A., A Simple Algorithm to Compute Comprehensive Gröbner Bases, Proc. ISSAC 2006 (2006), 326–331, ACM.

Schaller, S. C., Algorithmic Aspects of Polynomial Residue Class Rings, Thesis, University of Wisconsin at Madison (1975).

Schwartz, F., The Riquier–Janet Theory and its Applications to Nonlinear Evolution Equations, Physica 11D (1984), 243–251.Google Scholar

Schwartz, F., Reduction and Completion Algorithm for Partial Differential Equations, Proc. ISSA'92 (1992), 49–56, ACM.Google Scholar

Schwartz, F., Janet Bases for Symmetry Groups In: Buchberger, B., Winkler, F. (Eds.), Gröbner Bases and Application (1998), 221–234.

Shirayanagi, K., A Classification of Finite-dimensional Monomial AlgebrasProgr. Math. 94 (1990), 469–482, Birkhäuser.Google Scholar

Shirayanagi, K., Decision of Algebra Isomorphisms Using Gröbner Bases, Progr. Math. 109 (1993), 253–266, Birkhäuser.Google Scholar

Sit, W.Y., A Theory for Parametric Linear Systems, Proc. ISSAC'91 (1991), 112–121, ACM.

Sperner, E., Über einen kombinatorishen Satz von Macaulay und seine Anwerdungen auf die Theorie der Polynomideale, Abh. Math. Sem. Univ. Hamburg 7 (1930), 149–163.Google Scholar

Squier, C.C., Word Problems and a Homological Finiteness Condition for Monoids, J. Pure Appl. Algebra 49 (1987), 201–217.Google Scholar

Stillman, M., Tsai, H., Using SAGBA Bases for Computing Invariants, J. Pure Appl. Algebra 139 (1999), 285–302.Google Scholar

Szekeres, L., A Canonical Basis for the Ideals of a Polynomial Domain, Am. Math. Monthly 59 (1952), 379–386.Google Scholar

Sweedle, M., Ideal Bases and Valuation Rings, Manuscript (1986) available at http://math.usask.ca/fvk/Valth.html

Tamari, D., On a Certain Classification of Rings and Semigroups, Bull. A.M.S. 54 (1948), 153–158.Google Scholar

Thierry, N.M., Thomassé, S., Convex Cones and SAGBI Bases of Permutation Invariants. In: Invariant Theory in all Characteristics, CRM Proc. Lecture Notes, 35 (2004), 259–263, AMS.Google Scholar

Torstensson, A., Using Resultnats for SAGBI Basis Verification in the Univariate Polynomial Ring, J. Symb. Comp. 40 (2002), 1087–1105.Google Scholar

Torstensson, A., Ufnarovski, V., Öfverbeck, H., Canonical Bases for Subalgebras on Two Generators in the Univariate Polynomial Ring, Beiträge Algebra Geom. 43 (2005), 565–577.Google Scholar

Ufnarovski, V., A Growth Criterion for Graphs and Algebras Defined by Words, Math. Notes 31 (1983), 238–241.Google Scholar

Ufnarovski, V., On the use of Graphs for Computing a Basis, Growth and Hilbert Series of Associative Algebras, Math. Sb. 180 (1989), 1548–1560.Google Scholar

Ufnarovski, V., Combinatorial and Asymptotic Methods in Algebra. In: Kostrikin, A. I., Shafarevich, I. R. (Eds.), Algebra-VI (1995), Springer, 5–196.

Ufnarovski, V., Introduction to Noncommutative Gröbner Bases Theory. In: Buchberger, B., Winkler, F. (Eds.), Gröbner Bases and Application (1998), Cambridge University Press, 259–280.

Weispfenning, V., Gröbner Bases for Polynomial Ideals over Commutative Regular Rings, L. N. Comp. Sci. 378 (1987), 336–347, Springer.Google Scholar

Weispfenning, V., Comprehensive Gröbner Bases, J. Symb. Comp. 14 (1992), 1–29.Google Scholar

Weispfenning, V.Finite Gröbner Bases in Non-Noetherian Skew Polynomial Rings, Proc. ISSAC'92 (1992), 320–332, ACM.

Weispfenning, V., Canonical Comprehensive Gröbner Bases, J. Symb. Comp. 36 (2003), 669–683.Google Scholar

Weispfenning, V., Comprehensive Gröbner Bases and Regular Rings, J. Symb. Comp. 41 (2006), 285–296.Google Scholar

Wibmer, M.Gröbner Bases for Families of Affine or Projective Schemes, J. Symb. Comp. 42 (2007), 803–834.Google Scholar

Wiesinger-Widi, M.Gröbner Bases and Generalized Sylvester Matrices. PhD Thesis, Johannes Kepler University, Institute for Symbolic Computation, submitted 2014.

Zariski, O., Samuel, P., Commutative Algebra, Van Nostrand (1958).

Zacharias, G., Generalized Gröbner Bases in Commutative Polynomial Rings, Bachelor's Thesis, MIT (1978).

Zarkov, A., Solving Zero-dimensional Involutive Systems, Progr. Math. 143 (1996), 389–399, Birkhäuser.Google Scholar

Zarkov, A., Blinkov, Y., Involution Approach to Investing Polynomial Systems, Math. Comp. Simul. 42 (1996), 323–332.Google Scholar