AN APPROACH TO SEMIHYPERMODULES OVER SEMIHYPERRINGS

In this paper, we introduce semihypermodules over semihyperrings as a generalization of semimodules over semirings. Besides studying their properties, we introduce an equivalence relation on them and use it to define factor semihypermodules. Moreover, we discuss the (semi-)isomorphism theorems for semihypermodules and present some of their interesting applications. Finally, we project our results on semihyperrings and deduce the (semi-)isomorphism theorems for semihyperrings.