A right R-module M is called R-projective provided that it is projective relative to the right R-
module R. One of the parts of this thesis deals with the rings whose all nonsingular right …

A right R-module M is called R-projective provided that it is projective relative to the right R-
module RR. One of the parts of this thesis deals with the rings whose all nonsingular right …

Abstract A right R-module M is called R-projective provided that it is projective relative to the
right R-module R R. One of the parts of this thesis deals with the rings whose all nonsingular …

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 …

For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for
every cyclic right module N. The rings whose simple-injective right modules are injective are …

Proper classes (or exact structures) offer rich research topics due to their important role in
category theory. Motivated by the studies on opposite of injective modules, we introduce a …

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 …

It is shown that every pure-injective right module over a ring R is a direct sum of lifting
modules if and only if R is a ring of finite representation type and right local type. In …

We introduce and study a nontrivial generalization of uniserial modules and rings. A module
is called weakly uniserial if its submodules are comparable regarding embedding. Also, a …

Abstract A right R–module E over a ring R is said to be maximally injective in case for any
maximal right ideal m of R, every R–homomorphism f: m→ E can be extended to an R …