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
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
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