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...

A generalization of injective modules (noted GI-modules), distinct from p-injective modules, is introduced. Rings whose p-injective modules are GI are characterized. If M is a left GI-module, E = End(AM), then E/J(E) is von Neumann regular, where J(E) is the Jacobson radical of the ring E. A is semisimple Artinian if, and only if, every left A-module is GI. If A is a left p. p., left GI-ring su...

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.

Let $T=\biggl(\begin{matrix} A&0\\U&B\end{matrix}\biggr)$ be a formal triangular matrix ring, where $A$ and $B$ are rings $U$ is $(B, A)$-bimodule. We first give some computing formulas of projective, injective, flat $FP$-injective dimensions special left $T$-modules. Then we establish (weak) global $T$. It proven that (1) If $U_{A}$ $_{B}U$ $lD(A)\neq lD(B)$, then $lD(T)={\rm m...