Some Studies Of Homological Invariance Under Separable Frobenius Extensions

It is well-known that many homological properties are preserved under change of rings,especial excellent extension and Frobenius extension.In this paper,we mainly consider some homological invariant properties of GC-projectivity,GC-injectivity,Ding projectivity and FP-injectivity under sepa-rable Frobenius extensions.It is organized as followsIn section 1,we introduce the background and significance of the research Moreover,we give some preliminary results which are used in this paperIn section 2,we investigate the GC-projective modules under separable Frobenius extensions.We prove that the Gorenstein projectivity with respect to a semidualizing module are invariant under separable Frobenius extensions Moreover,we prove that GC-projective dimensions are invariant under sepa-rable Frobenius extensionsIn section 3,the object of our study is the GC-injective modules under separable Frobenius extensions.We give a proof that the Gorenstein injectivity with respect to a semidualizing module are invariant under separable Frobenius extensions.Moreover,we prove that GC-injective dimensions are invariant under separable Frobenius extensionsIn section 4,we prove that the Ding projectivity of a module and Ding projective dimensions are invariant under the separable Frobenius extensions Then,we prove that the FP-injectivity of a module and FP-injective dimen-sions are invariant under the separable Frobenius extensions...