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 RR. 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 $ R_ {R} $. This paper deals with the rings whose all nonsingular …

It is well-known that a ring R is right PF if and only if it is semiperfect and right self-injective
with essential right socle. In this note, it is shown that a ring R is right PF if and only if u. dim …

In this paper, we introduce and study the pure-direct-projective modules, that is the modules
M every pure submodule A of which with M/A isomorphic to a direct summand of M is a direct …

For a ring R, there are classical facts that R is right Noetherian if and only if every direct sum
of injective right R-modules is injective, and R is right Noetherian if and only if every …

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 …

In this paper, we introduce and study the dual notion of simple-direct-injective modules.
Namely, a right R-module M is called simple-direct-projective if, whenever A and B are …

This paper investigates the structure of cyclically pure (or C-pure) projective modules. In
particular, it is shown that a ring R is left Noetherian if and only if every C-pure projective left …

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 …