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

MathSciNet review:
1327054

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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 .

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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:
http://dx.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