An investigation on S-hypersystems over semihypergroups

Abstract

We recall the definition of an $S$-hypersystem and the fundamental normal homomorphism theorems on $S$-hypersystems. We introduce the concept of the category of $S$-hypersystems and study the product and coproduct of $S$-hypersystems. We prove that every $S$-pohypersystem is a subdirect product of subdirectly irreducible $S$-pohypersystems.