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C-Gorenstein projective, injective, flat modules and trivial ring extensions

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Published/Copyright: June 17, 2025
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Abstract

Let C be a semidualizing module over a commutative ring R and let R C be the trivial extension of R by C. We prove that (1) ( M , f ) is a Gorenstein projective R C -module if and only if M is a C-Gorenstein projective R-module; (2) [ M , g ] is a Gorenstein injective R C -module if and only if M is a C-Gorenstein injective R-module; (3) if R is a coherent ring, then ( M , f ) is a Gorenstein flat R C -module if and only if M is a C-Gorenstein flat R-module. Some applications of these results are given.

MSC 2020: 16D40; 16D50; 16E30

Award Identifier / Grant number: 12171230

Award Identifier / Grant number: 12271249

Funding statement: This research was supported by the National Natural Science Foundation of China (12171230, 12271249).

Acknowledgements

The author wants to express his gratitude to the referee for the very helpful comments and suggestions.

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Received: 2024-11-10
Revised: 2025-02-04
Accepted: 2025-03-12
Published Online: 2025-06-17

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