Year: 2025
Type: article
Abstract: The focus of this work was to establish relations between Gorenstein projective modules linked by right quasi-Frobenius extensions of rings. As applications, the right quasi-Frobenius extensions of (weakly) Gorenstein algebras, Cohen-Macaulay finite algebras and the Cohen-Macaulay free algebra were studied. Suppose that $ \Gamma $ was a right quasi-Frobenius extension of an Artin algebra $ \Lambda $ with $ \Gamma $ a completely faithful left $ \Lambda $-module. We demonstrated that if $ \Gamma $ exhibited (weakly) Gorenstein properties, then $ \Lambda $ did so. Additionally, under the condition of $ \Gamma $ being a separable extension of $ \Lambda $, the converse became valid.
Source: Electronic Research Archive
DOI: 10.3934/era.2025158
Authors: Juxiang Sun, Guoqiang Zhao
Institutions: Shangqiu Normal University, Hangzhou Dianzi University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,000
Awards: G3934287687, G5669366207
OpenAlex ID: W4411166703