On the heart of hypermodules

Abstract

This paper presents some types of hypermodules, associated to an arbitrary hypermodule, studying properties and characterizing their hearts. Also, we establish a few results concerning the sequence of heart, which can be associated to a hypermodule, in connection with subhypermodules generated by a non-empty set, by a union of subhypermodules or by the intersection of subhypermodules. Finally, we study several properties of $1$-hypermodules.