International Journal of Pure and Applied Mathematics Volume 98 No. 2 2015, 221-230 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v98i2.5 P A ijpam.eu A NOTE ON ORDERED QUASI-Γ-IDEALS IN INTRA-REGULAR PO-Γ-SEMIGROUPS M.Y. Abbasi 1 , Abul Basar 2 § 1,2 Department of Mathematics Jamia Millia Islamia New Delhi, 110 025, INDIA Abstract: In this paper, we characterize intra-regular po-Γ-semigroups through ordered quasi-Γ-ideals, ordered right Γ-ideals and ordered left Γ-ideals. Also, we investigate the po-Γ-semigroup in which the regular and intra-regular sub-Γ- semigroups are idempotents, left regular idempotents, commutative and idem- potents. AMS Subject Classification: 06F05, 20N02, 20M12 Key Words: po-Γ-semigroup, intra-regular po-Γ-semigroup, ordered quasi- Γ-ideal 1. Introduction The notion of Γ-semigroup was given by M. K. Sen [3] and that of the po-Γ- semigroup was introduced by Y. I. Kwon and S. K. Lee [16]. The notion of a quasi-ideal of semigroups was invented by O. Steinfeld[13]. Thereafter, quasi- ideals have been studied in different algebraic structures [4, 14]. N. Kehayopulu et al [7] defined and studied an ordered quasi-ideal in ordered semigroups. For regular ordered semigroups, left regular ordered semigroups and intra-regular ordered semigroups, we refer [8, 9, 10, 11, 15]. Received: September 12, 2014 c  2015 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author