On prime and semiprime generalized hyperaction of hypermonoid

Abstract

In this paper, we introduce the notion of generalized hyperaction of hypermonoid (GHS-act) on a set, establish its basic properties and prove some fundamental results. We also define the notion of prime, semiprime, irreducible and maximal GHS-subacts and characterize hypermonoid in terms of these GHS-subacts.

Connections between Hv-S-act, GHS-act and S-act

“…[15] Let A be a non-empty set and T (A) be the set of all transformations from A to A.Define • : T (A) × T (A) −→ P * (T (A)) by f • = f, , f for all f, ∈ T (A), where f represents the composition of two maps. Then (T (A), •) is a hypermonoid.…”