Weak multiplication semimodule

Abstract

The objective of this article is to introduce the concept of weak mutiplication semimodule and study several properties which are generalization of corresponding results for multiplication modules. We characterize full prime subsemimodules and full maximal subsemimodules and finally it is shown that in a finitely generated faithful weak multiplication semimodule, every proper full subsemimodule is contained in a maximal full subsemimodule.