On Ordered Quasi-Gamma-Ideals of Regular Ordered Gamma-Semigroups. (9th December 2013)

• Record Type: Journal Article
• Authors: Abbasi, M. Y.; Basar, Abul
• Other Names: Dascalescu Sorin Academic Editor.
• Is Part Of: Algebra. Volume 2013(2013)
• Publication Date: 2013-12-09
• Subjects: Algebra -- Periodicals; Algebra; Electronic journals; Periodicals; 512.005
• DOI: 10.1155/2013/565848
• Languages: English
• ISSNs: 2314-4106

Abstract

Abstract : We introduce the notion of ordered quasi-Γ -ideals of regular ordered Γ -semigroups and study the basic properties of ordered quasi-Γ -ideals of ordered Γ -semigroups. We also characterize regular ordered Γ -semigroups in terms of their ordered quasi-Γ -ideals, ordered right Γ -ideals, and left Γ -ideals. Finally, we have shown that (i) a partially ordered Γ -semigroup S is regular if and only if for every ordered bi-Γ -ideal B, every ordered Γ -ideal I, and every ordered quasi-Γ -ideal Q, we have B ∩ I ∩ Q ⊆ B Γ I Γ Q and (ii) a partially ordered Γ -semigroup S is regular if and only if for every ordered quasi-Γ -ideal Q, every ordered left Γ -ideal L, and every ordered right-Γ -ideal R, we have that R ∩ Q ∩ L ⊆ R Γ Q Γ L .