Weakly Projective and Weakly Injective Modules

On weakly projective and weakly injective modules

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...

Locally Injective Modules and Locally Projective Modules

Our dual notions “locally injective” and “locally projective” modules in Mod-R are good tools to study the relations between the singular, respectively cosingular, submodule of Hom R(M, W ) and the total Tot (M, W ). These notions have further interesting properties.

On Weakly Co-Hopfian Modules

Weakly Projective C∗-algebras

The noncommutative analog of an approximative absolute retract (AAR) is introduced, a weakly projective C∗-algebra. This property sits between being residually finite dimensional and projectivity. Examples and closure properties are considered.

Fp-injective and Weakly Quasi-frobenius Rings

The classes of FP -injective and weakly quasi-Frobenius rings are investigated. The properties for both classes of rings are closely linked with embedding of finitely presented modules in fp-flat and free modules respectively. Using these properties, we characterize the classes of coherent CF and FGF-rings. Moreover, it is proved that the group ring R(G) is FP -injective (weakly quasi-Frobenius...