A left FPF ring is a ring R such that every finitely generated faithful left R-module generates
the category of left R-modules. It is shown that such rings split into R= A⊕ B, where A is a …

In the seminal paper [1], Bass provided a number of characterizations of left perfect rings. In
the course of the proof of his" Theorem P", Bass implicitly showed that the ring R is left …

In analogy to the elementwise definition of von Neumann regular rings an $ R $-module $ M
$ is called regular if given any element $ m\in M $ there exists $ f\in {\operatorname {Hom} …

Introduction. A von Neumann regular ring A may be characterised by any one of the
following conditions:(a) every right (left) A-module is flat;(b) every right (left) A-module is p …

Throughout this paper we suppose that all rings and modules are unitary. By J we denote
always the Jacobson radical of a ring S. The left (right, resp.) annihilator of X is denoted by Z …

A ringRis said to be rightP-injective if every homomorphism of a principal right ideal toRis
given by left multiplication by an element ofR. This is equivalent to saying thatlr (a)= Rafor …

Koh [2] has shown that a commutative ring with identity is semiperfect if and only if every
simple right module has a projective cover. The purpose of this note is to show that the …

IYTRODCCTION 1: n~ onorphism rings of various types of modules have been objects of
extensive study in the recent past [2, 11, 14, 15, 18, 25, 261. In [15] Erika Mares introduced …

A ring R with unity is called right (left) self injective if the right (left) R-module R is injective
[7]. The purpose of this note is to prove the following: Let R be a prime ring with a maximal …

It is well-known that quasi-Frobenius rings are characterized by the property that all
propective right modules are injective, as well as by the property that all injective right …