Notes on Gorenstein Flat Modules
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In this paper, we explore conditions under which Gorenstein flat modules are Gorenstein projective. We prove that all countably presented strongly Gorenstein flat modules are Gorenstein projective over perfect rings. Moreover, we show that if the base ring R is \(\sum \)-pure injective as an R-module, then the class of Gorenstein flat modules coincides with the class of Gorenstein projective modules, and hence all modules have Gorenstein projective covers. And as a corollary, we give a characterization of coherent perfect rings by Gorenstein projective and Gorenstein flat modules.
KeywordsStrict Mittag–Leffler module Gorenstein projective module Gorenstein flat module
Mathematics Subject ClassificationPrimary 16D40 Secondary 16E05 16E30
This research was supported by NFSC (No. 11701408 and No. 11571165) and NSF of the Jiangsu Higher Education Institution (No. 16KJD1100 04). The authors would like to thank the referee for the very helpful comments and suggestions.
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