Note that, if X is a subset of a ring R, l (X)(resp. r (X)) is just the left (resp. right) annihilator of
X in R since(RR)*= RR. We call a ring R right PF if every faithful right R-module is a …

A ring $ R $ is regular [completely reducible] if and only if the character module of every left
$ R $-module is quasi-injective [quasiprojective]. Submodules of quasiprojective left $ R …

Abstract A ring\(R\) is said to be a left\(IF-(m, n)\) ring if every injective left\(R\)-module is\((m,
n)\)-flat. In this paper, several characterizations of left\(IF-(m, n)\) rings are investigated, some …

Responding to a question on right weakly semisimple rings due to Jain, Lopez-Permouth
and Singh, we report the existence of a non-right-Noetherian ring R for which every uniform …

II is shown that:(Ĩ) Let R be a simple riglil Noelhcriaii ring, then the following conditions are
equi\alent:(i) R is a riglit SI ring:(ii) I-'vcw cyclic singular right R-module is pseudo …

Endomorphism rings of nonfinitely generated free right i?-modules over a quasi-Frobenius
ring R are right self-injective but not left self-injective. A well-known example of a right self …

In this article, we provide several descriptions of w-coherent rings in terms of modules. We
show that a ring R is w-coherent if and only if every direct product of flat modules is w-flat. To …

Let $ R $ be a ring and $ M $ be an $ R $-module. In this paper we investigate modules $ M
$ such that every (simple) cosingular $ R $-module is $ M $-projective. We prove that every …

We introduce the concepts of (n, d)-injective and (n, d)-flat as generalizations of injective, flat
modules and homological dimensions, and use them to characterize right n-coherent rings …

A right $ R $-module $ M $ is called $ R $-projective provided that it is projective relative to
the right $ R $-module $ R_ {R} $. This paper deals with the rings whose all nonsingular …