Korean J. Math. Vol. 23 No. 3 (2015) pp.357-370
DOI: https://doi.org/10.11568/kjm.2015.23.3.357

On $(m,n)$-ideals of an ordered Abel-Grassmann groupoid

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Published: Sep 30, 2015
Keywords:
ordered AG-groupoid, left invertive law, left identity and (m, n)-ideal.
Mathematics Subject Classification:
20M10, 20N99.

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Faisal Yousafzai
School of Mathematical Sciences University of Science and Technology of China Hefei, China
Asad Khan
School of Mathematical Sciences University of Science and Technology of China Hefei, China
Aiyared Iampan
Department of Mathematics, School of Science University of Phayao Phayao 56000, Thailand

Abstract

In this paper, we introduce the concept of $(m,n)$-ideals in a non-associative ordered structure, which is called an ordered Abel-Grassmann's groupoid, by generalizing the concept of $(m,n)$-{ideals in an ordered semigroup [14]. We also study the} $(m,n)$-regular class of an ordered $\mathcal{AG}$-groupoid in terms of $(m,n)$-{ideals}.


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