SS-Injective modules and rings

الملخص EN

We introduce and investigate SS-injectivity as a generalization of both soc-injectivity and small injectivity.

A right module M over a ring R is said to be SS-N-injective (where N is a right R-module) if every R-homomorphism from a semisimple small submodule of N into M extends to N.

A module M is said to be SS-injective (resp.

strongly SS-injective), if M is SS-R-injective (resp.

SS-N-injective for every right R-module N).

Some characterizations and properties of (strongly) SS-injective modules and rings are given.

Some results on soc-injectivity are extended to SS-injectivity.