Some Characterizations of Intra-regular Abel-Grassmann Groupoids

Madad Khan; Saima Anis; Faizullah Faiz

doi:10.19026/rjaset.7.472

Research Journal of Applied Sciences, Engineering and Technology

Research Article | OPEN ACCESS

Some Characterizations of Intra-regular Abel-Grassmann Groupoids

¹Madad Khan, ¹Saima Anis and ²Faizullah Faiz

¹Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan
²NUST, Pindi, Pakistan

Research Journal of Applied Sciences, Engineering and Technology 2014 9:1848-1855

http://dx.doi.org/10.19026/rjaset.7.472 | © The Author(s) 2014

Received: June 07, 2013 | Accepted: August 05, 2013 | Published: March 05, 2014

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Abstract

In this study we introduce a new class of a non-associative algebraic structure namely intra-regular Abel Grassmann's groupoid (AG-groupoid in short). We apply generalized fuzzy ideal theory to this class and discuss its related properties. We introduce (∈,∈∨q_k) -fuzzy semiprime ideals in AG-groupoids and characterize it. Specifically we have characterized intra-regular AG-groupoids in terms of left, bi and two sided ideals and (∈,∈∨q_k) -fuzzy left, bi and two sided ideals. For support of our arguments we give examples of AG-groupoids. At the end we characterize intra-regular AG-groupoids using the properties of (∈,∈∨q_k) -fuzzy semiprime ideals.

Keywords:

AG-groupoid, (∈,∈∨q_k) -fuzzy ideals and (∈,∈∨q_k) -fuzzy bi-ideals, left invertive law, medial law, paramedial law,

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Competing interests

The authors have no competing interests.

Open Access Policy

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Copyright

The authors have no competing interests.

ISSN (Online): 2040-7467
ISSN (Print): 2040-7459

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