2020
DOI: 10.48550/arxiv.2004.02252
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When is $\mathfrak{m}:\mathfrak{m}$ an almost Gorenstein ring?

Abstract: Given a one-dimensional Cohen-Macaulay local ring (R, m, k), we prove that it is almost Gorenstein if and only if m is a canonical module of the ring m : m. Then, we generalize this result by introducing the notions of almost canonical ideal and gAGL ring and by proving that R is gAGL if and only if m is an almost canonical ideal of m : m. We use this fact to characterize when the ring m : m is almost Gorenstein, provided that R has minimal multiplicity. This is a generalization of a result proved by Chau, Got… Show more

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“…Besides the almost Gorenstein theory, the study of non-Gorenstein Cohen-Macaulay rings has been carried out under intense competition. One can also find other stratifications of Cohen-Macaulay rings in [3,4,5,9,15].…”
Section: Introductionmentioning
confidence: 91%
“…Besides the almost Gorenstein theory, the study of non-Gorenstein Cohen-Macaulay rings has been carried out under intense competition. One can also find other stratifications of Cohen-Macaulay rings in [3,4,5,9,15].…”
Section: Introductionmentioning
confidence: 91%