A note on self-dual AG-groupoids

Aziz-Ul-Hakim
Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan.
I. Ahmad
Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan.
M. Shah
Department of Mathematics, Government Post Graduate College Mardan, Pakistan.

\(^{2}\)Corresponding Author: iahmaad@hotmail.com

Copyright © 2016 Aziz-Ul-Hakim, I. Ahmad, M. Shah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2016.

Abstract

In this paper, we enumerate self-dual AG-groupoids up to order 6, and classify them on the basis of commutativity and associativity. A self-dual AG-groupoid-test is introduced to check an arbitrary AG-groupoid for a self-dual AG-groupoid. We also respond to an open problem regarding cancellativity of an element in an AG-groupoid. Some features of ideals in self-dual AG-groupoids are explored. Some desired algebraic structures are constructed from the known ones subject to certain conditions and some subclasses of self-dual AG-groupoids are introduced.

Keywords:

AG-groupoid, enumeration, connected set, ideal, anti-rectangular AG-groupoid.