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arXiv · 1704.05961

When is $R \ltimes I$ an almost Gorenstein local ring?

Shiro Goto·Shinya Kumashiro
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Abstract

Let $(R, \mathfrak{m}) $ be a Gorenstein local ring of dimension $d > 0$ and let $I$ be an ideal of $R$ such that $(0) \ne I \subsetneq R$ and $R/I$ is a Cohen-Macaulay ring of dimension $d$. There is given a complete answer to the question of when the idealization $A = R \ltimes I$ of $I$ over $R$ is an almost Gorenstein local ring.

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Shiro Goto, Shinya Kumashiro. 2017-04-20. When is $R \ltimes I$ an almost Gorenstein local ring?. https://arxiv.org/abs/1704.05961

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