Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-15T00:17:39.215Z Has data issue: false hasContentIssue false
  • English
  • Français

Idealizations of maximal Buchsbaum modules over a Buchsbaum ring

Published online by Cambridge University Press:  24 October 2008

Kikumichi Yamagishi
Kikumichi Yamagishi
Affiliation:
Himeji Dokkyo University, 7-2-1 Kamiono, Himeji 670, Japan
Get access Rights & Permissions [Opens in a new window]

Extract

Throughout this paper A denotes a Noetherian local ring with maximal ideal m and M denotes a finitely generated A-module. Moreover stands for the ith local cohomology functor with respect to m (cf. [10]). We refer to [15] for unexplained terminolog.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 3 , November 1988 , pp. 451 - 478
Copyright
Copyright © Cambridge Philosophical Society 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Aoyama, Y.. Some basic results on canonical modules. J. Math. Kyoto Univ. 23 (1983), 85–94.Google Scholar
[2]Goto, S.. On Buchsbaum rings. J. Algebra 67 (1980), 272–279.CrossRefGoogle Scholar
[3]Goto, S.. Buchsbaum rings of maximal embedding dimension. J. Algebra 76 (1982), 383–399.CrossRefGoogle Scholar
[4]Goto, S.. On the associated graded rings of parameter ideals in Buchsbaum rings. J. Algebra 85 (1983), 490–534.CrossRefGoogle Scholar
[5]Goto, S.. Noetherian local rings with Buchsbaum associated graded rings. J. Algebra 86 (1984), 336–384.CrossRefGoogle Scholar
[6]Goto, S.. A note on quasi-Buchsbaum rings. Proc. Amer. Math. Soc. 90 (1984), 511–516.CrossRefGoogle Scholar
[7]Goto, S.. Maximal Buchsbaum modules over regular local rings and a structure theorem for generalized Cohen–Macaulay modules. In Commutative Algebra and Combinatorics, Advanced Studies in Pure Math. no. 11 (North-Holland, 1987), pp. 39–64.CrossRefGoogle Scholar
[8]Goto, S. and Yamagishi, K.. The theory of unconditioned strong d-sequences and modules of finite local cohomology. (Preprint.)Google Scholar
[9]Goto, S. and Yamagishi, K.. Buchsbaum and quasi-Buchsbaum rings obtained by idealizations. (Unpublished manuscript, Japanese, 1982.)Google Scholar
[10]Grothendieck, A.. Local Cohomology. Lecture Notes in Math. vol. 41 (Springer-Verlag, 1967).Google Scholar
[11]Herzog, J. and Kunz, E.. Der kanonische Modul eines Cohen–Macaulay-Rings. Lecture Notes in Math. vol. 238 (Springer-Verlag, 1971).CrossRefGoogle Scholar
[12]Herzog, J., Simis, A. and Vasconcelos, W. V.. Approximation complexes of blowing-up rings. J. Algebra 74 (1982), 466–493.CrossRefGoogle Scholar
[13]Huneke, C.. On the symmetric and Rees algebra of an ideal generated by a d-sequence. J. Algebra 62 (1980), 268–275.CrossRefGoogle Scholar
[14]Huneke, C.. The theory of d-sequences and powers of ideals. Adv. in Math. 46 (1982), 249–279.CrossRefGoogle Scholar
[15]Nagata, M.. Local Rings. Tracts in Pure and Appl. Math. no. 13 (Interscience, 1962).Google Scholar
[16]Reiten, I.. The converse to a theorem of Sharp on Gorenstein modules. Proc. Amer. Math. Soc. 32 (1972), 417–420.CrossRefGoogle Scholar
[17]Renschuch, B., Stückrad, J. and Vogel, W.. Weitere Bemerkungen zu einem Problem der Schnittheorie und über ein Maß von A. Seidenberg für die Imperfektheit. J. Algebra 37 (1975), 447–471.CrossRefGoogle Scholar
[18]Schenzel, P.. Dualisierende Komplexe in der lokalen Algebra und Buchsbaum-Ringe. Lecture Notes in Math. vol. 907 (Springer-Verlag, 1982).CrossRefGoogle Scholar
[19]Sharpe, D. W. and Vámos, P.. Injective Modules. Cambridge Tracts in Math. no. 62 (Cambridge University Press, 1972).Google Scholar
[20]Stückrad, J. and Vogel, W.. Eine Verallgemeinerung der Cohen–Macaulay Ringe und Anwendungen auf ein Problem der Multiplizitätstheorie. J. Math. Kyoto Univ. 13 (1973), 513–528.Google Scholar
[21]Stückrad, J. and Vogel, W.. Toward a theory of Buchsbaum singularities. Amer. J. Math. 100 (1978), 727–746.CrossRefGoogle Scholar
[22]Stückrad, J. and Vogel, W.. On Segré products and applications. J. Algebra 54 (1978), 374–389.CrossRefGoogle Scholar
[23]Stückrad, J. and Vogel, W.. Buchsbaum Rings and Applications (Springer-Verlag, 1986).CrossRefGoogle Scholar
[24]Suzuki, N.. The Koszul complex of Buchsbaum modules. In Commutative Algebra and Algebraic Geometry, RIMS Kokyuroku 446 (Kyoto University, 1981), pp. 15–25.Google Scholar
[25]Suzuki, N.. On a basic theorem for quasi-Buchsbaum modules. Bull. Dept. Gen. Ed. Shizuoka College of Pharmacy 11 (1982), 33–40.Google Scholar
[26]Trung, N. V.. Toward a theory of generalized Cohen–Macaulay modules. Nagoya Math. J. 102 (1986), 1–49.CrossRefGoogle Scholar