SS-Injective Modules and Rings

Abstract

We introduce and investigate SS-injectivity as a generalization of both soc-injectivity and small injectivity. A right module over a ring is said to be SS- -injective (where is a right -module) if every -homomorphism from a semisimple small submodule of into extends to . A module is said to be SS-injective (resp. strongly SS-injective), if is SS- -injective (resp. SS- -injective for every right -module ). Some characterizations and properties of (strongly) SS-injective modules and rings are given. Some results on soc-injectivity are extended to SS-injectivity.

SAS-Injective Modules

“…Injective modules have been studied extensively, and several generalizations for these modules are given by many authors (see, for example, [2,10,9,7,8]).…”