REGULAR $\Gamma$-SO-RINGS

Abstract

A Γ-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a Γ-so-ring. In this paper we introduce the notions of irreducible, strongly irreducible ideals and a regular Γ-so-ring and we obtain the characteristics of them.