Note on Rightt Abelian Distributive AG-groupoids

Abstract

A magma that satisfies the left invertive law: ab · c = cb · a is called an AG-groupoid. The concept of right (left) abelian distributive groupoid (RAD resp. LAD) is extended to introduce some new subclasses of an AG-groupoid as right (left) abelian distributive AG-groupoid. The enumerations for these subclasses up to order 6 is provided using a modern computational techniques of GAP and various relations of these new subclasses are investigated with some other existing subclasses of AGgroupoids and other relevant algebraic structures. A manual procedure for the verification of an arbitrary finite AG-groupoid for RAD AG-groupoid is introduced. Various examples and counterexamples are produced with Prover-9 and Mace-4 to strengthen the validity of the produced results.