Frobenius Bimodules And Gorenstein Modules

In this thesis,the relationship between Frobenius bimodules and Gorenstein modules is discussed.In addition,the homology invariance of Dc-projective modules under(separable)Frobenius extension of rings is also considered.Firstly,let X and Y are two classes of R-modules,we mainly discuss the relationship between Frobenius bimodules and(X,Y)-Gorenstein projective(injective)modules,and(X,Y)Gorenstein projective(injective)dimensions of modules following the heritability of Frobenius functors.Secondly,let A is one class of R-modules,we mainly discuss the relationship between Frobenius bimodules and(F,A)-Gorenstein flat modules,and(F,A)-Gorenstein flat dimensions of modules following the heritability of Frobenius functors.Finally,we mainly discuss the homology invariance of Dc-projective modules and Dc-projective dimensions of modules under(separable)Frobenius extensions of rings,the work has generalized the existing conclusions.