Abstract
Let (R, m) be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by δR n(M) for each module M and for each integer n. We propose a conjecture asking if δR n(R/mℓ) = 0 for any positive integers n and ℓ. We prove that this is true provided the associated graded ring of R has depth not less than dim R - 1. Furthermore we show that there are only finitely many possibilities for a pair of positive integers (n, ℓ) for which δR n(R/mℓ) > 0.
| Original language | English |
|---|---|
| Pages (from-to) | 2641-2647 |
| Number of pages | 7 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 124 |
| Issue number | 9 |
| Publication status | Published - 1996 |
| Externally published | Yes |
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Keywords
- Cohen-Macaulay approximations
- Cohen-Macaulay modules
- Gorenstein ring
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
On the higher delta invariants of a Gorenstein local ring. / Yoshino, Yuji.
In: Proceedings of the American Mathematical Society, Vol. 124, No. 9, 1996, p. 2641-2647.Research output: Contribution to journal › Article
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TY - JOUR
T1 - On the higher delta invariants of a Gorenstein local ring
AU - Yoshino, Yuji
PY - 1996
Y1 - 1996
N2 - Let (R, m) be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by δR n(M) for each module M and for each integer n. We propose a conjecture asking if δR n(R/mℓ) = 0 for any positive integers n and ℓ. We prove that this is true provided the associated graded ring of R has depth not less than dim R - 1. Furthermore we show that there are only finitely many possibilities for a pair of positive integers (n, ℓ) for which δR n(R/mℓ) > 0.
AB - Let (R, m) be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by δR n(M) for each module M and for each integer n. We propose a conjecture asking if δR n(R/mℓ) = 0 for any positive integers n and ℓ. We prove that this is true provided the associated graded ring of R has depth not less than dim R - 1. Furthermore we show that there are only finitely many possibilities for a pair of positive integers (n, ℓ) for which δR n(R/mℓ) > 0.
KW - Cohen-Macaulay approximations
KW - Cohen-Macaulay modules
KW - Gorenstein ring
UR - http://www.scopus.com/inward/record.url?scp=21444458353&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=21444458353&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:21444458353
VL - 124
SP - 2641
EP - 2647
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 9
ER -