Rings with only finitely many isomorphism classes of indecomposable maximal Buchsbaum modules

Shiro GOTO; Kohji NISHIDA

doi:10.2969/jmsj/04030501

Shiro GOTO, Kohji NISHIDA

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JOURNAL FREE ACCESS

1988 Volume 40 Issue 3 Pages 501-518

DOI https://doi.org/10.2969/jmsj/04030501

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Published: 1988 Received: January 21, 1987 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: DTRECEIVED Details: Wrong : 19870127
Right : 19870121

Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Hiroyuki Tachikawa on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. Artin and J.-L. Verdier, Reflexive modules over rational double points, Math. Ann., 270 (1985), 79-82.
2) M. Auslander, Rational singularities and almost split sequences, Trans. Amer. Math. Soc., 293 (1986), 511-531.
3) R.-O. Buchweitz, G.-M. Gruel and F.-O. Schreyer, Cohen-Macaulay modules on hypersurface singularities II, preprint, 1986.
4) D. Eisenbud, Homological algebra on a complete intersection, with an application to group representations, Trans. Amer. Math. Soc., 260 (1980), 35-64.
5) D. Eisenbud and S. Goto, Linear free resolutions and minimal multiplicity, J. Algebra, 88 (1984), 89-133.
6) S. Goto, Maximal Buchsbaum modules over regular local rings and a structure theorem for generalized Cohen-Macaulay modules, to appear in Proceedings of Japan-U. S. Joint seminor on “Commutative algebra and Combinatrics”. 1985.
7) J. Herzog and E. Kunz, Der kanonische Modul eines Cohen-Macaulay-Rings, Lecture Notes in Math., 238, Springer, 1971.
8) J. Herzog, Ringe mit nur endlich vielen Isomorphieklassen von maximalen unzerlegbaren Cohen-Macaulay-Moduln, Math. Ann., 233 (1978), 21-34.
9) K. Kiyek and G. Steinke, Einfache Kurvensingularitäten in beliebiger Charakteristik, Arch. Math., 45 (1985), 565-573.
10) H. Knörrer, Cohen-Macaulay modules on hypersurface singularities I, preprint, 1986.
11) N. Popescu, Abelian categories with applications to rings and modules, Academic Press, New York-London, 1973.
12) I. Reiten, Cohen-Macaulay modules over isolated singularities, preprint.
13) J. Stückrad and W. Vogel, Eine Verallgemeinerung der Cohen-Macaulay Ringe und Anwendungen auf ein Problem der Multiplizitätstheorie, J. Math. Kyoto Univ., 13 (1973), 513-528.
14) I. Reiten, Toward a theory of Buchsbaum singularities, Amer. J. Math., 100 (1978), 727-746.
15) I. Reiten, Buchsbaum rings and applications, VEB Deutscher Verlag der Wissenschaften, 1987.

Right : [1] M. Artin and J. -L. Verdier, Reflexive modules over rational double points, Math. Ann., 270 (1985), 79-82.
[2] M. Auslander, Rational singularities and almost split sequences, Trans. Amer. Math. Soc., 293 (1986), 511-531.
[3] R. -O. Buchweitz, G.-M. Gruel and F. -O. Schreyer, Cohen-Macaulay modules on hypersurface singularities II, preprint, 1986.
[4] D. Eisenbud, Homological algebra on a complete intersection, with an application to group representations, Trans. Amer. Math. Soc., 260 (1980), 35-64.
[5] D. Eisenbud and S. Goto, Linear free resolutions and minimal multiplicity, J. Algebra, 88 (1984), 89-133.
[6] S. Goto, Maximal Buchsbaum modules over regular local rings and a structure theorem for generalized Cohen-Macaulay modules, to appear in Proceedings of Japan-U. S. Joint seminor on “Commutative algebra and Combinatrics”. 1985.
[7] J. Herzog and E. Kunz, Der kanonische Modul eines Cohen-Macaulay-Rings, Lecture Notes in Math., 238, Springer, 1971.
[8] J. Herzog, Ringe mit nur endlich vielen Isomorphieklassen von maximalen unzerlegbaren Cohen-Macaulay-Moduln, Math. Ann., 233 (1978), 21-34.
[9] K. Kiyek and G. Steinke, Einfache Kurvensingularitäten in beliebiger Charakteristik, Arch. Math., 45 (1985), 565-573.
[10] H. Knörrer, Cohen-Macaulay modules on hypersurface singularities I, preprint, 1986.
[11] N. Popescu, Abelian categories with applications to rings and modules, Academic Press, New York-London, 1973.
[12] I. Reiten, Cohen-Macaulay modules over isolated singularities, preprint.
[13] J. Stückrad and W. Vogel, Eine Verallgemeinerung der Cohen-Macaulay Ringe und Anwendungen auf ein Problem der Multiplizitätstheorie, J. Math. Kyoto Univ., 13 (1973), 513-528.
[14] J. Stückrad and W. Vogel, Toward a theory of Buchsbaum singularities, Amer. J. Math., 100 (1978), 727-746.
[15] J. Stückrad and W. Vogel, Buchsbaum rings and applications, VEB Deutscher Verlag der Wissenschaften, 1987.

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