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Toward a theory of generalized Cohen-Macaulay modules

Published online by Cambridge University Press:  22 January 2016

Ngô Viêt Trung
Ngô Viêt Trung*
Affiliation:
Institute of Mathematics, Viên Toán hoc, Box 631, Bò’ Hô, Hanoi, Vietnam
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Throughout this paper, A denotes a noetherian local ring with maximal ideal m and M a finitely generated A-module with d: = dim M≥1.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 102 , June 1986 , pp. 1 - 49
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

[ 1 ] Abhyankar, S. S., Local rings of high embedding dimension, Amer. J. Math., 89 (1967), 1073–1077.Google Scholar
[ 2 ] Auslander, M, Buchsbaum, D. A., Codimension and multiplicity, Ann. of Math., 68 (1958), 625–657.Google Scholar
[ 3 ] Brodmann, M., Endlichkeit von lokalen Kohomologie-Moduln arithmetischer Aufblasungen, Preprint.Google Scholar
[ 4 ] Brodmann, M., Kohomologische Eigenschaften von Aufblasungen an lokal vollstándigen Durchschnitten, Preprint.Google Scholar
[ 5 ] Buchsbaum, D. A., Complexes in local ring theory, In: Some aspects of ring theory, C.I.M.E., Rome 1965.Google Scholar
[ 6 ] Cuong, N. T., Schenzel, P., Trung, N. V., Verallgemeinerte Cohen-Macaulay-Moduln, Math. Nachr., 85 (1978), 57–73.Google Scholar
[ 7 ] Goto, S., On the Cohen-Macaulayfication of certain Buchsbaum rings, Nagoya Math. J., 80 (1980), 107–116.Google Scholar
[ 8 ] Goto, S., Buchsbaum rings of maximal embedding dimension, J. Algebra, 76 (1982), 494–508.CrossRefGoogle Scholar
[ 9 ] Goto, S., On the associated graded rings of parameter ideals in Buchsbaum rings, Preprint.Google Scholar
[10] Goto, S., Noetherian local rings with Buchsbaum associated graded rings, J. Algebra, 86 (1984), 336–384.Google Scholar
[11] Goto, S., Blowing-up of Buchsbaum rings, Proceedings, Durham symposium on Com mutative Algebra, 140–162, London Math. Soc. Lect. Notes, 72 (1982).Google Scholar
[12] Goto, S., Shimoda, Y., On Rees algebras over Buchsbaum rings, J. Math. Kyoto Univ., 20 (1980), 691–708.Google Scholar
[13] Herzog, J., Simis, A., Vasconcelos, W. V., Approximation complexes of blowing-up rings, J. Algebra, 74 (1982), 466–493.Google Scholar
[14] Huneke, C., On the symmetric and Rees algebra generated by a d-sequenee, J. Algebra, 62 (1980), 268–275.Google Scholar
[15] Huneke, C., The theory of d-sequences and powers of ideals, Adv. in Math., 46 (1982), 249–279.CrossRefGoogle Scholar
[16] Northcott, D. G., Rees, D., Reductions of ideals in local rings, Proc. Cambridge Phil. Soc., 50 (1954), 145–158.Google Scholar
[17] Sally, J., Cohen-Macaulay local rings of maximal embedding dimension, J. Algebra, 56 (1979), 168–183.Google Scholar
[18] Schenzel, P., Multiplizitäten in verallgemeinerten Cohen-Macaulay-Moduln, Math. Nachr., 88 (1979), 295–306.Google Scholar
[19] Schenzel, P., Regular sequences in Rees and symmetric algebras, Manuscripta Math., 35 (1981), 173–193.CrossRefGoogle Scholar
[20] Stückrad, J., Vogel, W., Theorie der Buchsbaum-Moduln, to appear.Google Scholar
[21] Stückrad, J., Über die kohomologische Charakterisierung von Buchsbaum-Moduln, Math. Nachr., 95 (1980), 265–272.CrossRefGoogle Scholar
[22] Stückrad, J., 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
[23] Stückrad, J., Vogel, W., Toward a theory of Buchsbaum singularities, Amer. J. Math., 100 (1978), 727–746.Google Scholar
[24] Trung, N. V., Über die Übertragung der Ringeigenschaften zwischen R und R[u]/(F), Math. Nachr., 92 (1979), 215–229.CrossRefGoogle Scholar
[25] Trung, N. V., Some criteria for Buchsbaum modules, Monatsh. Math., 90 (1980), 331–337.Google Scholar
[26] Trung, N. V., On the associated graded ring of a Buchsbaum ring, Math. Nachr., 107 (1982), 209–220.CrossRefGoogle Scholar
[27] Trung, N. V., Absolutely superficial sequence, Math. Proc. Cambridge Phil. Soc., 93 (1983), 35–47.Google Scholar
[28] Valla, G., Certain graded algebras are always Cohen-Macaulay, J. Algebra, 42 (1976), 537–548.Google Scholar
[29] Valla, G., On the symmetric and Rees algebras of an ideal, Manuscripta Math., 30 (1980), 239–255.Google Scholar
[30] Vogel, W., Über eine Vermutung von D. A. Buchsbaum, J. Algebra, 23 (1973), 106–112.Google Scholar
[31] Vogel, W., A non-zero-divisor characterization of Buchsbaum modules, Michigan Math. J., 28 (1981), 147–152.CrossRefGoogle Scholar
[32] Ooishi, A., Openness of loci, p-excellent rings and modules, Hiroshima Math. J., 10 (1980), 419–436.CrossRefGoogle Scholar