Gorenstein invariants under right Quasi-Frobenius extensions

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 $ \Gamma $ was a right quasi-Frobenius extension of an Artin algebra $ \Lambda $ with $ \Gamma $ a completely faithful left $ \Lambda $-module. We demonstrated that if $ \Gamma $ exhibited (weakly) Gorenstein properties, then $ \Lambda $ did so. Additionally, under the condition of $ \Gamma $ being a separable extension of $ \Lambda $, the converse became valid.