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September 10, 2025Open Access

On extension closure of E-Gorenstein flat modules

Key Points

The class of gorenstein flat right R-modules is closed under extensions, allowing for projective resolution.
This finding, which validates an open question posed by Gao and Zhong, demonstrates significant closure properties.
The introduction of coresolved gorenstein flat modules shows that these classes are also projectively resolving.
Additionally, the class remains closed under transfinite extensions, enhancing the understanding of module properties.

Abstract

Let R be an arbitrary ring and E an injectively resolving class of left R -modules. We prove that the class of 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 E -projectively coresolved Gorenstein flat modules, and prove that the class of E -projectively coresolved Gorenstein flat right R -modules is projectively resolving and closed under transfinite extensions.

On extension closure of E-Gorenstein flat modules

Key Points

Abstract

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