Module theory is an important tool for many different branches of mathematics, as well as
being an interesting subject in its own right. Within module theory, the concept of injective …

Since the discovery of the existence of the injective hull of an arbitrary module
independently in 1952 by Shoda and in 1953 by Eckmann and Schopf, there have been …

Let M and N be two modules. M is called automorphism N-invariant if for any essential
submodule A of N, any essential monomorphism f: A→ M can be extended to some g∈ Hom …

In this paper we extend several results known for reduced rings to reduced modules. We
prove that for a semiprime module or a module with zero Jacobson radical, the concepts of …

The idea that the socle plays a dual role to that of the Jacobson radical is not new, although
rarely used or mentioned. There are, of course many radicals besides the Jacobson radical …

All rings are assumed to be associative and (except for nil-rings and some stipulated cases)
to have nonzero identity elements. Expressions such as a “Noetherian ring” mean that the …

A module M has the property (V) il for every K< M, KIM and me MK, any submodule-L
maximal, with respect to the property that it contains K but does not contain the element m, is …

Introduction. A ring R is called a left SI-ring if every singular left R-module is injective. SI-
rings were introduced and studied by KR Goodearl. In this paper we say that a left R-module …

This survey covers material in Referativnyi Zhurnal Matematika and is a continuation of AV
Mikhalev's survey in Algebra. Topology. Geometry, Vol. 12 (Itogi Nauki i Tekhniki (1974)) …

Extending a result of Boyle and Goodearl in [1] on V-rings it was shown in Yousif [11] that a
generalized V-module (GV-module) has Krull dimension if and only if it is noetherian. Our …