On generalized Gorenstein local rings

Fuente: arXiv
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Main Authors: Goto, Shiro, Kumashiro, Shinya
Format: Preprint
Published: 2022
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author Goto, Shiro
Kumashiro, Shinya
author_facet Goto, Shiro
Kumashiro, Shinya
contents In this paper, we introduce generalized Gorenstein local (GGL) rings. The notion of GGL rings is a natural generalization of the notion of almost Gorenstein rings, which can thus be treated as part of the theory of GGL rings. For a Cohen-Macaulay local ring $R$, we explore the endomorphism algebra of the maximal ideal, the trace ideal of the canonical module, Ulrich ideals, and Rees algebras of parameter ideals in connection with the GGL property. We also give numerous examples of numerical semigroup rings, idealizations, and determinantal rings of certain matrices.
format Preprint
id arxiv_https___arxiv_org_abs_2212_12762
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle On generalized Gorenstein local rings
Goto, Shiro
Kumashiro, Shinya
Commutative Algebra
13H10, 13C13, 13B02
In this paper, we introduce generalized Gorenstein local (GGL) rings. The notion of GGL rings is a natural generalization of the notion of almost Gorenstein rings, which can thus be treated as part of the theory of GGL rings. For a Cohen-Macaulay local ring $R$, we explore the endomorphism algebra of the maximal ideal, the trace ideal of the canonical module, Ulrich ideals, and Rees algebras of parameter ideals in connection with the GGL property. We also give numerous examples of numerical semigroup rings, idealizations, and determinantal rings of certain matrices.
title On generalized Gorenstein local rings
topic Commutative Algebra
13H10, 13C13, 13B02
url https://arxiv.org/abs/2212.12762