Characterization of Regularity of Posemigroups by High-Quasi-Ideals

Subject Areas : Mathematical Analysis

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

Received: 2022-04-18 Accepted : 2022-08-28 Published : 2022-10-01

Keywords: Posemigroup, High-quasi-ideal, Regular, High-bi-ideal,

Abstract :

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.