Let G be a finite group and k be a field of characteristic p. We investigate the homotopy category K(Inj kG) of the category C(Inj kG) of complexes of injective (= projective) kG-modules. If G is a p-group, this category is equivalent to the derived category Ddg(C(BG; k)) of the cochains on the classifying space; if G is not a p-group it has better properties than this derived category. The ord...

This note investigates modules having quasi-injective and duo submodules. We introduce a new generalization of C_1-module. The main method that was adopted in this is how to obtain submodule N M the characteristic Quasi-injective. investigate relationship between pseudo-injective module Quasi-injective property Finally, we anti-hopfian module.

The purpose of this paper is to further the study of weakly injective and weakly projective modules as a generalization of injective and projective modules. For a locally q.f.d. module M , there exists a module K ∈ σ[M ] such that K ⊕N is weakly injective in σ[M ], for any N ∈ σ[M ]. Similarly, if M is projective and right perfect in σ[M ], then there exists a module K ∈ σ[M ] such that K ⊕ N i...

In this paper we study some properties of GC -projective, injective and flat modules, where C is a semidualizing module and we discuss some connections between GC -projective, injective and flat modules , and we consider these properties under change of rings such that completions of rings, Morita equivalences and the localizations.

This paper is an exposition of the so-called injective Morita contexts (in which the connecting bimodule morphisms are injective) and Morita α-contexts (in which the connecting bimodules enjoy some local projectivity in the sense of ZimmermannHuisgen). Motivated by situations in which only one trace ideal is in action, or the compatibility between the bimodule morphisms is not needed, we introd...

This paper contains new and previously known results on modules that are close to direct projective injective modules. The main presented with proofs.

There are remarkable relations between the graded homological dimensions and the ordinary homological dimensions. In this paper, we study the injective dimension of a complex of graded modules and derive its some properties. In particular, we define the $^*$dualizing complex for a graded ring and investigate its consequences.