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2017 Quasi-Gorensteinness of extended Rees algebras
Youngsu Kim
J. Commut. Algebra 9(4): 507-544 (2017). DOI: 10.1216/JCA-2017-9-4-507

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.

Citation

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Youngsu Kim. "Quasi-Gorensteinness of extended Rees algebras." J. Commut. Algebra 9 (4) 507 - 544, 2017. https://doi.org/10.1216/JCA-2017-9-4-507

Information

Published: 2017
First available in Project Euclid: 14 October 2017

zbMATH: 06797097
MathSciNet: MR3713526
Digital Object Identifier: 10.1216/JCA-2017-9-4-507

Subjects:
Primary: 13A30, 13H10

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.9 • No. 4 • 2017
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