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A note on Gorenstein projective and Gorenstein flat modules
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We prove that all Gorenstein projective modules are Gorenstein flat if and only each Gorenstein projective module has finite Gorenstein flat dimension. As applications, some characterizations of strongly CM-free rings are established and an affirmative answer to a question posed by Wang [Colloq. Math. 170 (2022) 1–13] is obtained.
Title: A note on Gorenstein projective and Gorenstein flat modules
Description:
We prove that all Gorenstein projective modules are Gorenstein flat if and only each Gorenstein projective module has finite Gorenstein flat dimension.
As applications, some characterizations of strongly CM-free rings are established and an affirmative answer to a question posed by Wang [Colloq.
Math.
170 (2022) 1–13] is obtained.
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