A Study of Anti-Commutativity in AG-Groupoids

Abstract

A magma that also satisfies the left invertive law, (ab) c = (cb) a is called an AG-groupoid. Generally, an AG-groupoid is a non-associative structure lying midway between a groupoid and a commutative semigroup. We consider the notion of anticommutativity in AG-groupoids and investigate some of their properties. A new subclass of AG-groupoids as rectangular AG-groupoid is introduced and investigated. A variety of examples and counter examples are produced using the latest computational techniques of GAP, Mace4 and Prover9.