On extension closure of E-Gorenstein flat modules

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.