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 …

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 …

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 …