On the theory and applications of G-dimension with respect to a semidualizing module

Author:

Miranda-Neto Cleto B.1ORCID,Souza Thyago S.2ORCID

Affiliation:

1. Departamento de Matemática, Universidade Federal da Paraíba, 58051-900, João Pessoa, PB, Brazil

2. Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, 58429-970, Campina Grande, PB, Brazil

Abstract

We contribute to the theory of G-dimension relative to a semidualizing module [Formula: see text], in connection to the properties of a module being totally [Formula: see text]-reflexive, [Formula: see text]-[Formula: see text]-torsionless, and [Formula: see text]-[Formula: see text]-syzygy, where [Formula: see text] is an integer. We extend several known results, and for an integer [Formula: see text] we introduce the class of [Formula: see text]-[Formula: see text]-Gorenstein rings. We also consider [Formula: see text]-duals and initiate the study of [Formula: see text]-valued derivation modules over a local ring [Formula: see text] of low depth; if [Formula: see text] and [Formula: see text] is a three-dimensional Gorenstein domain, we find a bound for the number of generators and we propose a question when [Formula: see text] is general.

Funder

Conselho Nacional de Desenvolvimento Cientifico e Tecnologico

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Algebra and Number Theory

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On reduced G-perfection and horizontal linkage;Communications in Algebra;2023-09-13

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