A COMPREHENSIVE NOTE ON WEAK-COMMUTATIVE AG-GROUPOIDS

Abstract

A magma satisfying the left invertive law, ab · c = cb · a is known as an AG-groupoid or left-almost semi-group. The concept of bi-commutative groupoid arising in [N. Bobeica et al. (2010)] is extended to introduce a new subclass of AG-groupoid as weak-commutative AG-groupoid. Latest computational techniques of Mace-4 and GAP are used for generating various non-associative examples to prove existence of this class. Enumeration of this subclass up to order 6 is also provided. Various relations of this class with other known algebraic structures are established. Further, the newly introduced class of weak-commutative AG-groupoids is decomposed by defining some congruences.

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