A note on self-dual AG-groupoids

JPRM-Vol. 1 (2016), Issue 1, pp. 01 – 15 Open Access Full-Text PDF
Aziz-Ul-Hakim, I. Ahmad, M. Shah
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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