It is shown that every finitely generated right R-module is almost injective if and only if every cyclic right R-module is almost injective, if and only if R/J(R) is a right SV-ring with Loewy(RR) ≤ 2 and there is a finite ...
The notion of simple-direct-injective modules which are a generalization of injective modules unifies C2 and C3-modules. In the present paper, we introduce the notion of the semisimple-direct-injective module which gives ...
We investigate the semirings over which all simple semimodules are injective. In ring and module theory, the rings with an analogous condition are called V-rings. Therefore it is natural to call the semirings under ...