A \(\Gamma\)-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 \(\Gamma\)-so-ring. In this paper we introduce the notions of semiprime ideal and \(p\)-system in \(\Gamma\)-so-rings and we obtain the characteristics between them.

A Gamma-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 Gamma-so-ring. In this paper we introduce the notion of prime ideal for Gamma-so-rings and obtain the characteristics of primeideals of Gamma-so-rings.

A \(\Gamma\)-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 \(\Gamma\)-so-ring. In this paper we introduce the notions of dense and annihilator ideals of \(\Gamma\)-so-rings and obtain the Green's relations in Partial \(\Gamma\) semirings.

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