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A note on self-dual AG-groupoids

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Title: A note on self-dual AG-groupoids

Authors: Aziz-Ul-Hakim, I. Ahmad, M. Shah

Journal: Journal of Prime Research in Mathematics

HEC Recognition History
Category From To
Y 2023-07-01 2024-09-30
Y 2022-07-01 2023-06-30
Y 2021-07-01 2022-06-30
Y 2020-07-01 2021-06-30

Publisher: Abdus Salam School of Mathematical Sciences, GC University

Country: Pakistan

Year: 2016

Volume: 1

Issue: 1

Language: English

Keywords: self-dual AG-groupoidsAG-groupoids

Categories
Universal Algebra (10) Groupoids (5) Abstract Algebra (137) Algebra (130) Mathematics (5170)

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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