Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Auslander's $ \delta$-invariants of Gorenstein local rings

Author: Songqing Ding
Journal: Proc. Amer. Math. Soc. 122 (1994), 649-656
MSC: Primary 13H10; Secondary 13A15, 13C14
MathSciNet review: 1203983
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let (R, $ \mathfrak{m}$, k) be a Gorenstein local ring with associated graded ring $ G(R)$. It is conjectured that for any integer $ n > 0$, Auslander's $ \delta $-invariant $ \delta (R/{\mathfrak{m}^n})$ of $ R/{\mathfrak{m}^n}$ equals 1 if and only if $ {\mathfrak{m}^n}$ is contained in a parameter ideal of R. In an earlier paper we showed that the conjecture holds if $ G(R)$ is Cohen-Macaulay. In this paper we prove that the conjecture has an affirmative answer if depth $ G(R) = \dim R - 1$ and R is gradable. We also prove that if R is not regular and depth $ G(R) \geq \dim R - 1$, then $ \delta (R/{\mathfrak{m}^2}) = 1$ if and only if R has minimal multiplicity.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13H10, 13A15, 13C14

Retrieve articles in all journals with MSC: 13H10, 13A15, 13C14

Additional Information

Article copyright: © Copyright 1994 American Mathematical Society