On Ideal Elements in Poe-AG-groupoid

Abstract

In this paper we introduce the concept of ideal elements in poe-AG-groupoid and give some characterizations and properties of their ideal elements. So we consider some results concerning ideals in poe-semigroups and investigate them in poe-AG-groupoids. Also, the class of ideal elements of poe-AG-groupoids are studied, certain intrinsic and basic properties of poe-AG-groupoids including: ideal, bi-ideal, interior ideal, prime, semiprime, intra-regular elements and etc. are studied as well. The corresponding results on poe-semigroups can be also obtained as application of the results of this paper.