Document Type : Special issue editorial

Author

• A. R. Shabani

Department of Mathematics Imam Khomaini Naval Academy, Nowshahr, Iran

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.

Keywords

• AG-groupoid
• poe-semigroup
• poe-AG-groupoid
• ideal element
• intrior ideal element
• prime
• semiprime
• intra-regular
• g-regular
• filter element
• quasi-commutative