A note on self-dual AG-groupoids

Authors

  • 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.

Keywords:

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

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.

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Published

2016-12-31

Issue

Vol. 12 No. 1 (2016): Journal of Prime Research in Mathematics

Section

Regular

How to Cite

A note on self-dual AG-groupoids. (2016). Journal of Prime Research in Mathematics, 12(1), 01 – 15. https://jprm.sms.edu.pk/index.php/jprm/article/view/116