The purpose of this paper is to further the study of weakly injective and weakly projective
modules as a generalization of injective and projective modules. For a locally qfd module …

We show that ifRis a semiperfect ring with essential left socle andrl (K)= Kfor every small
right idealKofR, thenRis right continuous. Accordingly some well-known classes of rings …

Let R be a ring, na fixed nonnegative integer and In (Fn) the class of all left (right) R-modules
of injective (flat) dimension at most n. A left R-module M (resp., right R-module F) is called n …

‎ We call a ring $ R $ right generalized semiperfect if every simple right $ R $-module is an
epimorphic image of a flat right $ R $-module with small kernel‎,‎ that is‎,‎ every simple right $ R …

A famous theorem of algebra due to Osofsky states that “if every cyclic left R-module is
injective, then R is semisimple”. Therefore, a natural question of this sort is:“What is the class …

For a fixed given right R-module M, so-called M-flat left R-modules are investigated, which
are flat relative to short exact sequences in the subcategory σ [M] subgenerated by M. The …

Rings have a unit and modules are unitary. Here follow the concepts which are studied in
this note. If R is a ring if M is a left Λ-module then M is left coperfect if the dcc (descending …

Let R be a ring. A right R-module N is called an Mp-injective module if any homomorphism
from an M-cyclic submodule of M can be extended to M. In this paper, we extend this notion …

Throughout, R is an associative ring with identity and all modules are unitary. Unless
otherwise specified, s is a class of some right R-modules which is closed under …