For a given class of R-modules Q, module M is called Q-copure Baer injective if any map from left ideal R into can be extended to M. Depending on the this concept both dualization and generalization pure injectivity. We show that every embedded as submodule module. Certain types rings are characterized using properties modules. example ring Q-coregular only R-module injective.

We develop a suitable version of the stable module category of a finite group G over an arbitrary commutative ring k. The purpose of the construction is to produce a compactly generated triangulated category whose compact objects are the finitely presented kG-modules. The main idea is to form a localisation of the usual version of the stable module category with respect to the filtered colimits...

If R̂ is the pure-injective hull of a valuation ring R, it is proved that R̂ ⊗R M is the pure-injective hull of M , for every finitely generated Rmodule M . Moreover R̂ ⊗R M ∼= ⊕1≤k≤nR̂/AkR̂, where (Ak)1≤k≤n is the annihilator sequence of M . The pure-injective hulls of uniserial or polyserial modules are also investigated. Any two pure-composition series of a countably generated polyserial module a...

In the present paper new criteria for classes of FP -injective and weakly quasi-Frobenius rings are given. Properties of both classes of rings are closely linked with embedding of finitely presented modules in fp-flat and free modules respectively. Using these properties, we describe classes of coherent CF and FGF-rings. Moreover, it is proved that the group ring R(G) is FP -injective (resp. we...

A right R-module M is called a generalized q.f.d. module if every M-singular quotient has finitely generated socle. In this note we give several characterizations to this class of modules by means of weak injectivity, tightness, and weak tightness that generalizes the results in [25], Theorem 3. In particular, it is shown that a module M is g.q.f.d. iff every direct sum of M -singular M -inject...

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...