Ideals in Ordered Γ-Semirings

Abstract

In this paper, we introduce the notion of k-ideal, m−k ideal, prime ideal, maximal ideal, filter, irreducible ideal, strongly irreducible ideal in ordered Γ-semirings, study the properties of ideals in ordered Γ-semirings and the relations between them. We characterize m − k ideals using derivation of ordered Γ-semirings and prove that every ideal in a mono regular ordered Γ-semiring is a prime ideal and field ordered Γ-semiring is simple.

Keywords

• ordered γ-semiring
• integral ordered γ-semiring
• regular or- dered γ-semiring
• mono ordered γ-semiring
• prime ideal
• maximal ideal
• k- ideal
• m− k ideal
• filter
• irreducible ideal
• strongly irreducible ideal
• 16a09
• 06f25