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Synergy in the Theories of Gröbner Bases and Path Algebras

Published online by Cambridge University Press:  20 November 2018

Daniel R. Farkas ,
C. D. Feustel  and
Edward L. Green
Daniel R. Farkas
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, U.S.A.
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Abstract

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A general theory for Grôbner basis in path algebras is introduced which extends the known theory for commutative polynomial rings and free associative algebras.

Keywords

13P1016D1568Q40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 4 , 01 August 1993 , pp. 727 - 739
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Beckmann, P. and Stuckrad, J., The concept of Groebner algebras, J. Symp. Comp. 10(1990), 465–479.Google Scholar
2. Bergman, G., The diamond lemma for ring theory, Adv. Math. 29(1978), 178–218.Google Scholar
3. Buchberger, B., An algorithm for finding a basis for the residue class ring of a zero-dimensional ideal, Ph.D. Thesis, University of Innsbruck, 1965.Google Scholar
4. Farkas, D. and Green, E. L., Do subspaces have distinguished bases?, Rocky Mountain Journal, to appear.Google Scholar
5. Feustel, C. D., Green, E. L., Kirkman, E. and Kuzmanovich, J., Constructing projective resolutions, to appear.Google Scholar
6. Mora, F., Grôbner basis for non-commutative polynomial rings, Proc. AAECC3, L.N.C.S. 229(1986).Google Scholar
7. Mora, T., Seven variations on standard bases, Report Dip. Mat. Univ. Genoa, (1988).Google Scholar
8. Mora, T., Grôbner bases and the word problem, preprint.Google Scholar
9. Pauer, F. and Pfeifholder, M., The theory of Grôbner bases, L'Enseigment Mathématique, (2) 34(1988), 215–232.Google Scholar
10. Ringel, C., Tame Algebras and Integral Quadratic Forms, LNM 1099, Springer- Verlag, Berlin-Heidelberg- New York-Tokyo, 1984.Google Scholar
11. Robbiano, L., Introduction to the theory of Grôbner bases, Queen's Papers in Pure and Applied Math, (80) V(1988).Google Scholar
12. Robbiano, L., The theory of graded structures, J. Symb. Comp. 2(1986).Google Scholar
13. Sweedler, M., Ideal bases and valuation rings, unpublished.Google Scholar
14. Ufnarovskii, V., A growth criterion for graphs and algebras defined by words, Mat. Zameti 31(1980), 465–472; Math. Notes 37(1982), 238–241.Google Scholar