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Idealizations of maximal Buchsbaum modules over a Buchsbaum ring

Published online by Cambridge University Press:  24 October 2008

Kikumichi Yamagishi
Affiliation:
Himeji Dokkyo University, 7-2-1 Kamiono, Himeji 670, Japan

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
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Aoyama, Y.. Some basic results on canonical modules. J. Math. Kyoto Univ. 23 (1983), 8594.Google Scholar
[2]Goto, S.. On Buchsbaum rings. J. Algebra 67 (1980), 272279.CrossRefGoogle Scholar
[3]Goto, S.. Buchsbaum rings of maximal embedding dimension. J. Algebra 76 (1982), 383399.CrossRefGoogle Scholar
[4]Goto, S.. On the associated graded rings of parameter ideals in Buchsbaum rings. J. Algebra 85 (1983), 490534.CrossRefGoogle Scholar
[5]Goto, S.. Noetherian local rings with Buchsbaum associated graded rings. J. Algebra 86 (1984), 336384.CrossRefGoogle Scholar
[6]Goto, S.. A note on quasi-Buchsbaum rings. Proc. Amer. Math. Soc. 90 (1984), 511516.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. 3964.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 (Unpublished manuscript, Japanese, 1982.)Google Scholar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), 466493.CrossRefGoogle Scholar
[13]Huneke, C.. On the symmetric and Rees algebra of an ideal generated by a d-sequence. J. Algebra 62 (1980), 268275.CrossRefGoogle Scholar
[14]Huneke, C.. The theory of d-sequences and powers of ideals. Adv. in Math. 46 (1982), 249279.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), 417420.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), 447471.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), 513528.Google Scholar
[21]Stückrad, J. and Vogel, W.. Toward a theory of Buchsbaum singularities. Amer. J. Math. 100 (1978), 727746.CrossRefGoogle Scholar
[22]Stückrad, J. and Vogel, W.. On Segré products and applications. J. Algebra 54 (1978), 374389.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. 1525.Google Scholar
[25]Suzuki, N.. On a basic theorem for quasi-Buchsbaum modules. Bull. Dept. Gen. Ed. Shizuoka College of Pharmacy 11 (1982), 3340.Google Scholar
[26]Trung, N. V.. Toward a theory of generalized Cohen–Macaulay modules. Nagoya Math. J. 102 (1986), 149.CrossRefGoogle Scholar