Journal of Commutative Algebra

Quasi-Gorensteinness of extended Rees algebras

Youngsu Kim

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Abstract

Let $R$ be a Noetherian local ring and $I$ an $R$-ideal. It is well known that, if the associated graded ring ${gr} _I(R)$ is Cohen-Macaulay (Gorenstein), then so is $R$, but in general, the converse is not true. In this paper, we investigate the Cohen-Macaulayness and Gorensteinness of the associated graded ring ${gr} _I(R)$ under the hypothesis that the extended Rees algebra $R[It,t^{-1}]$ is quasi-Gorenstein or the associated graded ring ${gr} _I(R)$ is a domain.

Article information

Source
J. Commut. Algebra, Volume 9, Number 4 (2017), 507-544.

Dates
First available in Project Euclid: 14 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.jca/1507946697

Digital Object Identifier
doi:10.1216/JCA-2017-9-4-507

Mathematical Reviews number (MathSciNet)
MR3713526

Zentralblatt MATH identifier
06797097

Subjects
Primary: 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

Keywords
Extended Rees algebra associated graded ring quasi-Gorenstein ring Cohen-Macaulay ring

Citation

Kim, Youngsu. Quasi-Gorensteinness of extended Rees algebras. J. Commut. Algebra 9 (2017), no. 4, 507--544. doi:10.1216/JCA-2017-9-4-507. https://projecteuclid.org/euclid.jca/1507946697


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