Quasi-injective and quasi-projective modules over hereditary Noetherian prime rings

Characterization of rings using direct-projective modules and direct-injective modules

Semisimple, semiperfect, and perfect rings are characterized by quasiprojective modules and quasiprojective covers over them.

/pdf/characterization-of-rings-using-quasiprojective-modules-iii-473ab7n5pm.pdf

Characterization of rings using quasiprojective modules. III

In this paper we study modules coinvariant under automorphisms of their projective covers. We first provide an alternative, and in fact, a more succinct and conceptual proof for the result that a module $M$ is invariant under automorphisms of its injective envelope if and only if given any submodule $N$ of $M$, any monomorphism $f:N\rightarrow M$ can be extended to an endomorphism of $M$ and then, as a dual of it, we show that over a right perfect ring, a module $M$ is coinvariant under automorphisms of its projective cover if and only if for every submodule $N$ of $M$, any epimorphism $\varphi: M\rightarrow M/N$ can be lifted to an endomorphism of $M$.

Modules which are coinvariant under automorphisms of their projective covers

Une propriété d'exactitude du foncteur hom et quelques caractérisations de modules projectifs

Characterization of rings using quasiprojective modules

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Characterization of rings using quasiprojective modules

Characterization of rings using quasiprojective modules. III