Characterization of Regularity of Posemigroups by High-Quasi-Ideals

الموضوعات :

Mohammadmahdi Shamivand ¹ (Department of Mathematics, Borujerd Branch, Islamic Azad University, Borujerd, Iran.)

تاريخ الإرسال : 17 الإثنين , رمضان, 1443 تاريخ التأكيد : 01 الأحد , صفر, 1444 تاريخ الإصدار : 05 السبت , ربيع الأول, 1444

الکلمات المفتاحية: Posemigroup, High-quasi-ideal, Regular, High-bi-ideal,

ملخص المقالة :

A semigroup S is called a posemigroup if S is equipped with an ordering relation\ ≤ " such that a ≤ b in S implies xa ≤ xb and ax ≤ bx, for all x 2 S. In what followswe study necessary and sufficient conditions that a posemigroup S to be regular, interms of certain conditions of Q∗ S, the semigroup of high-quasi-ideals of S. This studygives us a characterization method of the regular posemigroups.