ON PROPERTIES OF VARIOUS MORPHISMS IN THE CATEGORIES OF GENERAL KRASNER HYPERMODULES

Abstract

In a recent paper entitled Pre-semihyperadditive Categories, we introduced some categories in which for objects A and B, the class of all morphisms from A to B denoted by Mor(A, B), admits an algebraic hyperstructures such as semihypergroup or hypergroup.  Then after defining and fixing a general Krasner hyperring R, we introduced and studied the categories of general Krasner R-hypermodules, _R\(\mathcal{G}\).mod, \(_{R_{s}}\)\(\mathbf{\mathcal{G}}\).mod, \(_{R_{w}}\)\(\mathbf{\mathcal{G}}\).mod and etc.  In this paper we present some properties of multi-valued homomorphisms as morphisms of these categories and study various concepts related to these morphisms in connection with the fundamental relation of their domain or codomain.