One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition,
where a module M is called a C3-module if whenever A and B are direct summands of M …

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 …

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 …

Harada [4] introduced the notions of mininjective modules and rings as follows: Let M and N
be right R-modules. M is said to be min-N-injective if for every simple submodule K of N, and …

In this paper, we study the notions (strongly) soc-injective,(strongly) simple-injective and
(strongly) mininjective modules in σ [M]. For any module N in σ [M], N is strongly mininjective …

In this paper, we study the notions (strongly) soc-injective,(strongly) simple-injective and
(strongly) mininjective modules in σ [M]. For any module N in σ [M], N is strongly mininjective …

A right R-module M is called to satisfy condition (𝒞) if, for every s∈ S= End R (M) and s≠ 0,
there exists n∈ ℕ such that sn≠ 0 and if Ker (sn) is a direct summand of M, then IM (sn) is a …

In this paper, we study the notions (strongly) soc-injective,(strongly) simple-injective and
(strongly) mininjective modules in σ [M]. For any module N in o [M], N is strongly mininjective …