On the higher delta invariants

of a Gorenstein local ring

Author:
Yuji Yoshino

Journal:
Proc. Amer. Math. Soc. **124** (1996), 2641-2647

MSC (1991):
Primary 13C14, 13D02, 13H10, 16G50

DOI:
https://doi.org/10.1090/S0002-9939-96-03376-X

MathSciNet review:
1327054

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by for each module and for each integer . We propose a conjecture asking if for any positive integers and . We prove that this is true provided the associated graded ring of has depth not less than . Furthermore we show that there are only finitely many possibilities for a pair of positive integers for which .

**[1]**M. Auslander, R. -O. Buchweitz,*The homological theory of maximal Cohen-Macaulay approximations*, Soc. Math. de France, Mem.**38**(1989), 5--37. MR**91h:13010****[2]**M. Auslander, S. Ding, Ø. Solberg,*Liftings and weak liftings of modules*, J. Algebra**156**(1993), 273--317. MR**94d:16007****[3]**S. Ding,*Cohen-Macaulay approximations and multiplicities*, J. Algebra**153**(1992), 172--188. MR**94c:13024****[4]**S. Ding,*A note on the index of Cohen-Macaulay local rings*, Comm. Algebra**21**(1993), 53--71. MR**94b:13014****[5]**S. Ding,*The associated graded ring and the index of a Gorenstein local ring*, Proc. of the Amer. Math. Soc.**120**(1994), 1029--1033. MR**94f:13014****[6]**J. Herzog,*On the index of a homogenous Gorenstein ring*, Contemporary Math.**159**(1994), 95--102. MR**95b:13031****[7]**A. Shida,*On indices of local rings along local homomorphisms*, Preprint, Nagoya Univ. (1994).

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Additional Information

**Yuji Yoshino**

Affiliation:
Institute of Mathematics, Faculty of Integrated Human Studies, Kyoto University, Yoshida-Nihonmatsu, Sakyo-ku, Kyoto 606-01, Japan

Email:
yoshino@math.h.kyoto-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-96-03376-X

Keywords:
Cohen-Macaulay modules,
Gorenstein ring,
Cohen-Macaulay approximations

Received by editor(s):
January 20, 1995

Received by editor(s) in revised form:
March 9, 1995

Dedicated:
To the memory of Professor Maurice Auslander

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1996
American Mathematical Society