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.
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