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arXiv · 2111.13338

When are the rings $I:I$ Gorenstein?

Naoki Endo·Shiro Goto·Shin-ichiro Iai·Naoyuki Matsuoka
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Abstract

Let $I ~(\ne A)$ be an ideal of a $d$-dimensional Noetherian local ring $A$ with $\operatorname{ht}_AI \ge 2$, containing a non-zerodivisor. The problem of when the ring $I:I=\operatorname{End}_AI$ is Gorenstein is studied, in connection with the problem of the Gorensteinness in Rees algebras $\mathcal{R}_A(Q^d)$ for certain parameter ideals $Q$ of $A$, that was closely explored by the preceding paper of the second and third authors. Examples are given.

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Naoki Endo, Shiro Goto, Shin-ichiro Iai, Naoyuki Matsuoka. 2021-11-26. When are the rings $I:I$ Gorenstein?. https://arxiv.org/abs/2111.13338

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