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A note on right abelian distributive AG-groupoids

Author(s)
Bashar Khan Department of Mathematics, University of Malakand, Pakistan
Imtiaz Ahmad Department of Mathematics, University of Malakand, Pakistan
Amanullah Department of Mathematics, University of Malakand, Pakistan
Muhammad Rashad Department of Mathematics, University of Malakand, Pakistan
Abstract
A magma that satisfies the left invertive law: ab ¢ c = cb ¢ a is called an AG-groupoid. The concept of right (left) abelian distributive groupoid (RAD resp. LAD) is extended to introduce some new subclasses of an AG-groupoid as right (left) abelian distributive AG-groupoid. The enumerations for these subclasses up to order 6 is provided using a modern computational techniques of GAP and various relations of these new subclasses are investigated with some other existing subclasses of AGgroupoids and other relevant algebraic structures. A manual procedure for the verification of an arbitrary finite AG-groupoid for RAD AG-groupoid is introduced. Various examples and counterexamples are produced with Prover-9 and Mace-4 to strengthen the validity of the produced results.
Publication Details
Page(s) 45-64
DOI DOI not available
Published Journal: Punjab University Journal of Mathematics, Volume: 52, Issue: 11, Year: 2020

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Keywords
AG-groupoid, Paramedial, abelian distributive, locally associative AG-groupoid
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