We define below a notion for modules which is dual to that of faithful, and a notion of “fully
divisible” which generalizes that of injectivity. We show that the bicommutator of a cofaithful …

In this paper all rings have an identity, and all modules are unitary left. R-modules. The
category of left K-modules is denoted by RJL In recent papers [1, 3, 5, 7], a module M is …

Let M be a left module over a ring R. A submodule N of M is called locally split in M if for
each x EN there exists a homomorphism h: Mt N such that h (x)= x. It is shown that if N is …

In this paper we introduce 𝒯-noncosingular modules. Rings for which all right modules are𝒯-
noncosingular are shown to be precisely those for which every simple right module is …

In [2 1, Fuchs has shown that R is a test module for quasiinjective modules. He showed that
if M is a right R-module, M is quasi-injective if and only if for each right ideal K of R, every R …

Let R be a ring with 1 and let Q denote the maximal left quotient ring of R [6]. In a recent
paper [12], Wei called a (left). R-module M divisible in case HomR (Q, N)≠ 0 for each …

We study the modules RU which are injective over their endomorphism ring and we apply
the results obtained to faithfully balanced bimodules and rings with Morita duality. We also …

In this paper we introduce T-noncosingular modules. Rings for which all right modules are T-
noncosingular are shown to be precisely those for which every simple right module is …

It is proved that if R is an associative ring that is cotorsion as a left module over itself, and J is
the Jacobson radical of R, then the quotient ring R/J is a left self-injective von Neumann …

Publisher Summary This chapter describes the quasi-simple modules and weak transitivity.
If RVD be an R, D-bimodule, where D is a division ring R is a ring and RV is a uniform …