2014•arXiv (Cornell University)Open access

Enumeration of Bi-commutative AG-groupoids

Muhammad Sami Rashad, Imtiaz Ahmad, Muhammad Shah, Arsham Borumand Saeid

Abstract

A groupoid satisfying the left invertive law: $ab\cdot c=cb\cdot a$ is called an AG-groupoid and is a generalization of commutative semigroups. We consider the concept of bi-commutativity in AG-groupoids and thus introduce left commutative AG-groupoids, right commutative AG-groupoids and bi-commutative AG-groupoids.

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Key concepts: Commutative property, Mathematics, Generalization, Enumeration, Pure mathematics, Commutative ring, Discrete mathematics, Algebra over a field