A note on right abelian distributive AG-groupoids | [Punjab University Journal of Mathematics • 2020]

Author(s):

1. Bashar Khan: Department of Mathematics, University of Malakand, Pakistan

2. Imtiaz Ahmad: Department of Mathematics, University of Malakand, Pakistan

3. Amanullah: Department of Mathematics, University of Malakand, Pakistan

4. 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.

Page(s): 45-64

DOI: DOI not available

Published: Journal: Punjab University Journal of Mathematics, Volume: 52, Issue: 11, Year: 2020

Keywords:

AGgroupoid , Paramedial , abelian distributive , locally associative AGgroupoid

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