Generalizing Artinian rings, a ring R is said to have right restricted minimum condition (r.
RMC r. RMC, for short) if R/A is an Artinian right R-module for any essential right ideal A of …

A theorem due to Warfield states that “a ring R is left serial if and only if every (finitely
generated) projective left R-module is serial” and a theorem due to Tuganbaev states that “a …

Let R be a ring with an identity element. We prove that R is right Kasch if and only if injective
hull of every simple right R-modules is neat-flat if and only if every absolutely pure right R …

The purpose of this paper is to examine conditions under which (1) a left noetherian left V-
ring is left hereditary and (2) a left noetherian left V-ring is a two sided noetherian V-ring. For …

It is shown that a principal right ideal domain, having the property that every right $ R $
module has a maximal submodule must be simple. Strong conditions satisfied by these rings …

Let R be a ring. An R-module M is finitely annihilated if the annihilator of M is the annihilator
of a finite subset of M. It is proved that if R has right socle S then the ring R/S is right Artinian …

Publisher Summary This chapter discusses the max rings, V-rings, and rings and modules
related to V-rings. All rings are associative and have nonzero identity elements. A module is …

Recently, in a series of papers “simple” versions of direct-injective and direct-projective
modules have been investigated. These modules are termed as “simple-direct-injective” and …

Throughout this paper, R denotes an associative ring with identity and all modules are
unitary. A right R-module M is called principally injective briefly, p-injective) if for any …

We prove that a ring R has a module M whose domain of projectivity consists of only some
injective modules if and only if R is a right noetherian right V-ring. Also, we consider …