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arXiv · 1504.08014

Testing for the Gorenstein property

Olgur Celikbas·Sean Sather-Wagstaff
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Abstract

We answer a question of Celikbas, Dao, and Takahashi by establishing the following characterization of Gorenstein rings: a commutative noetherian local ring $(R,\mathfrak m)$ is Gorenstein if and only if it admits an integrally closed $\mathfrak m$-primary ideal of finite Gorenstein dimension. This is accomplished through a detailed study of certain test complexes. Along the way we construct such a test complex that detect finiteness of Gorenstein dimension, but not that of projective dimension.

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Olgur Celikbas, Sean Sather-Wagstaff. 2015-04-29. Testing for the Gorenstein property. https://arxiv.org/abs/1504.08014

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