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http://dx.doi.org/10.4134/BKMS.b200056

GORENSTEIN MODULES UNDER FROBENIUS EXTENSIONS  

Kong, Fangdi (Department of Applied Mathematics Lanzhou University of Technology)
Wu, Dejun (Department of Applied Mathematics Lanzhou University of Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.6, 2020 , pp. 1567-1579 More about this Journal
Abstract
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 HomR(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.
Keywords
Frobenius extension; ${\mathcal{X}}$-Gorenstein module; super finitely presented module; Ding module; PGF-module;
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