Left Transitive AG-groupoids
Group Theory
2016-06-21 v3
Abstract
An AG-groupoid is an algebraic structure that satisfies the left invertive law: (ab)c =(cb)a. We prove that the class of left transitive AG-groupoids (AG-groupoids satisfying the identity, ab.ac = bc) coincides with the class of T2-AG-groupoids. We also develop a simple procedure to test whether an arbitrary groupoid is left transitive AG-groupoid or not. Further we prove that, (i). Every left transitive AG-groupoid is transitively commutative AG-groupoid (ii) For left transitive AG-groupoid the properties of flexibility, right alternativity, AG*, right nuclear square, middle nuclear square and commutative semigroup are equivalent.
Cite
@article{arxiv.1402.5296,
title = {Left Transitive AG-groupoids},
author = {Muhammad Rashad and Imtiaz Ahmad and Muhammad Shah and Z. U. A. Khuhro},
journal= {arXiv preprint arXiv:1402.5296},
year = {2016}
}
Comments
This paper has been withdrawn by the author(s) due to crucial errors in the table on page 2