When is $R⋉I$ an almost Gorenstein local ring?

Abstract

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

7 pages

References in corpus (3)

• On the almost Gorenstein property in Rees algebras of contracted ideals
• Almost Gorenstein Rees algebras of $p_g$-ideals, good ideals, and powers of the maximal ideals
• On the almost Gorenstein property of determinantal rings

Cited by in corpus (2)

• Generalized Gorenstein Arf rings
• Characterization of generalized Gorenstein rings