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Bass number characterization of surjective Buchsbaum modules

Published online by Cambridge University Press:  24 October 2008

Kikumichi Yamagishi
Kikumichi Yamagishi
Affiliation:
College of Liberal Arts, Himeji Dokkyo University, Kamiono 7-2-1, Himeji 670, Japan Dedicated to Sadako Yamagishi on her 70th birthday
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Extract

Throughout this paper (A, m, k) denotes a Noetherian local ring and stands for the ith local cohomology functor with respect to m. We refer to [9] for unexplained terminology.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 2 , September 1991 , pp. 261 - 279
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Bass, H.. On the ubiquity of Gorenstein rings. Math. Z. 82 (1963), 8–28.CrossRefGoogle Scholar
[2]Foxby, H.-B.. A homological theory of complexes of modules. Preprint (1981).CrossRefGoogle Scholar
[3]Goto, S.. On Buchsbaum rings. J. Algebra 67 (1980), 272–279.CrossRefGoogle Scholar
[4]Goto, S.. Buchsbaum rings of maximal embedding dimension. J. Algebra 76 (1982), 383–399.CrossRefGoogle Scholar
[5]Goto, S.. On the surjectivity criterion for Buchsbaum modules. Proc. Amer. Math. Soc. 108 (1990), 641–646.CrossRefGoogle Scholar
[6]Grothendieck, A.. Local Cohomology. Lecture Notes in Math. vol. 41 (Springer-Verlag, 1967).Google Scholar
[7]Herzog, J. and Kunz, E.. Der kanonische Modul eines Cohen–Macaulay–Rings. Lecture Notes in Math. vol. 238 (Springer-Verlag, 1971).CrossRefGoogle Scholar
[8]Herzog, J., Simis, A. and Vasconcelos, W. V.. Approximation complexes of blowing-up rings. J. Algebra 74 (1982), 466–493.CrossRefGoogle Scholar
[9]Nagata, M.. Local Rings. Tracts in Pure and Appl. Math. no. 13 (Interscience, 1962).Google Scholar
[10]Roberts, P.. Homological invariants of modules over commutative rings. Séminaire de Math. Sup. no. 72 (Les Press de l'université de Montréal, 1980).Google Scholar
[11]Schenzel, P.. Dualisierende Komplexe in der lokalen Algebra und Buchsbaum–Ringe. Lecture Notes in Math. vol. 907 (Springer-Verlag, 1982).CrossRefGoogle Scholar
[12]Sharpe, D. W. and Vámos, P.. Injective Modules. Cambridge Tracts in Math. no. 62 (Cambridge University Press, 1972).Google Scholar
[13]Stückrad, J.. Über die kohomologische Charakterisierung von Buchsbaum-Moduln. Math. Nachr. 95 (1980), 265–272.CrossRefGoogle Scholar
[14]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
[15]Stückrad, J. and Vogel, W.. Toward a theory of Buchsbaum singularities. Amer. J. Math. 100 (1978), 727–746.CrossRefGoogle Scholar
[16]Stückrad, J. and Vogel, W.. Buchsbaum Rings and Applications (Springer-Verlag, 1986).CrossRefGoogle Scholar
[17]Vasconcelos, W. V.. Ideals generated by R-sequences. J. Algebra 6 (1967), 309–316.CrossRefGoogle Scholar
[18]Yamagishi, K.. Idealizations of maximal Buchsbaum modules over a Buchsbaum ring. Math. Proc. Cambridge Philos. Soc. 104 (1988), 451–478.CrossRefGoogle Scholar