• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1567-1579
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• 2020

Let R ⊂ S be a Frobenius extension of rings and M a left S-module and let 𝓧 be a class of left R-modules and 𝒚 a class of left S-modules. Under some conditions it is proven that M is a 𝒚-Gorenstein left S-module if and only if M is an 𝓧-Gorenstein left R-module if and only if S ⊗_R M and Hom_R(S, M) are 𝒚-Gorenstein left S-modules. This statement extends a known corresponding result. In addition, the situations of Ding modules, Gorenstein AC modules and projectively coresolved Gorenstein flat modules are considered under Frobenius extensions.