A COMPARATIVE STUDY OF REPEATED AG-GROUPOIDS

Abstract

A magma that satisfies the left invertive law: ab · c = cb · a is called an AG-groupoid.  The concept of “repeated LA-semigroup” that arise in various papers, which satisfies the two identities: (t · u)(v · w) = (uu)· (vv), ∀t, u, v, w (Inner Repeated), (t · u)(v · w) = (tt) · (ww), ∀t, u, v, w (Outer Repeated) is investigated. The enumerations for these subclasses up to order 6 is provided using the modern computational techniques of GAP. Furthermore, various relations of these subclasses are investigated with some other existing subclasses of AG-groupoids and with other relevant algebraic structures. Various examples and counterexamples are produced with Prover-9 and Mace-4 to strengthen the validity of the produced results.

Keywords : AG-groupoid, LA-semigroups, paramedial, abelian distributive groupoid, inner and outer repeated