Work

On extension closure of $\mathcal{E}$-Gorenstein flat modules

Year: 2025

Type: article

Abstract: Let R be an arbitrary ring and \mathcal{E} an injectively resolving class of left R -modules. We prove that the class of \mathcal{E} -Gorenstein flat right R -modules is closed under extensions, and hence projectively resolving. This answers an open question in Gao and Zhong [Rocky Mountain J. Math. 54 (2024), 143–160] affirmatively. As a consequence, we get that this class is covering. In addition, we introduce the notion of \mathcal{E} -projectively coresolved Gorenstein flat modules, and prove that the class of \mathcal{E} -projectively coresolved Gorenstein flat right R -modules is projectively resolving and closed under transfinite extensions.

Source: Rendiconti del Seminario Matematico della Università di Padova

DOI: 10.4171/rsmup/183

Authors: Zenghui Gao, Zhaoyong Huang, Yucheng Wang

Institutions: Chengdu University of Information Technology, Nanjing University

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4413225049

FWCI:

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