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Abstract
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Article Information:
Some Characterizations of Intra-regular Abel-Grassmann Groupoids
Madad Khan, Saima Anis and Faizullah Faiz
Corresponding Author: Madad Khan
Submitted: June 07, 2013
Accepted: August 05, 2013
Published: March 05, 2014 |
Abstract:
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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 (&isin, &isin v qk) -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 (&isin, &isin v qk) -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 (&isin, &isin v qk)-fuzzy semiprime ideals.
Key words: AG-groupoid, (&isin, &isin v qk) -fuzzy ideals and (&isin, &isin v qk) -fuzzy bi-ideals, left invertive law, medial law, paramedial law, ,
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Cite this Reference:
Madad Khan, Saima Anis and Faizullah Faiz, . Some Characterizations of Intra-regular Abel-Grassmann Groupoids. Research Journal of Applied Sciences, Engineering and Technology, (9): 1848-1855.
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ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
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