A Study on Cheban Abel-Grassmann's Groupoids

Abstract

An AG-groupoid also called a Left-almost semigroup is a magma satisfying the law, uv ·w = wv ·u ∀u, v, w. In this paper, the concept of Cheban AG-groupoid is developed and investigated as a subclass of AG-groupoid. Various non-associative examples and counterexamples are constructed by the recent computational techniques of Mace-4, GAP and Prover-9. Cheban AG-groupoids are enumerated up to order 6 and various relations of this class are established with already existing subclasses of AG-groupoids. Furthermore, ideals in Cheban AG-groupoid are introduced and investigated.