Characterizing the Ordered AG-Groupoids Through the Properties of Their Different Classes of Ideals

Abstract

In this article, we have presented some important charcterizations of the ordered non-associative semigroups in relation to their ideals. We have initially characterized the ordered AG-groupoid through the properties of the their ideals, then we characterized the two important classes of these AG-groupoids, namely the regular and intragregular non-associative AG-groupoids. Our aim is also to encourage the research and the maturity of the associative algebraic structures by studying a class of non-associative and non-commutative algebraic structures called the ordered AG-groupoid.

Keywords

• Ordered AG-groupoids
• left (right, interior, quasi-, bi-, generalized bi-) ideals
• regular (intraregular) ordered AG-groupoids