When is 𝑅⋉𝐼 an almost Gorenstein local ring?

Goto, Shiro; Kumashiro, Shinya

doi:10.1090/proc/13835

When is $R \ltimes I$ an almost Gorenstein local ring?
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Proc. Amer. Math. Soc. 146 (2018), 1431-1437 Request permission

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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