Gorenstein invariants under right Quasi-Frobenius extensions

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Abstract

The focus of this work was to establish relations between Gorenstein projective modules linked by right quasi-Frobenius extensions of rings. As applications, the right quasi-Frobenius extensions of (weakly) Gorenstein algebras, Cohen-Macaulay finite algebras and the Cohen-Macaulay free algebra were studied. Suppose that Γ was a right quasi-Frobenius extension of an Artin algebra Λ with Γ a completely faithful left Λ-module. We demonstrated that if Γ exhibited (weakly) Gorenstein properties, then Λ did so. Additionally, under the condition of Γ being a separable extension of Λ, the converse became valid.

Keywords

right quasi-Frobenius extension / Gorenstein projective module / CM-finite algebra / CM-free algebra / Gorenstein algebra

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