Nearly Injective Semimodules

Abstract

An injectivity in the category of semimodules over semiring was studied by many authors recently. On the other hand, the concept of injectivity, in the category of modules over ring, was generalized in many different directions. In particular, injective modules relative to preradical were some of those generalizations.        As an analogue to module theory, in this paper, we introduce  and investigate the notion of "injective semimodule relative to Jacobson radical (namely nearly injective semimodule)".