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Cancellative Elements in Finite AG-groupoids
ISSN: 2149 - 1402
Publisher: author
Cancellative Elements in Finite AG-groupoids
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Science General
ARTICLE-FACTOR
1.3
Article Basics Score: 2
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International Category Code (ICC):
ICC-1402
Publisher: Journal Of New Theory Naim Çağman
International Journal Address (IAA):
IAA.ZONE/214975511402
eISSN
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2149 - 1402
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Abstract
An Abel-Grassmann’s groupoid (brie y AG-groupoid) is a groupoid S satisfying the left invertive law: (xy)z=(zy)x for all x,y,z∈S. In the present paper, we discuss the left and right cancellative property of elements of the finite AG-groupoid S. For an AG-groupoid with left identity it is known that every left cancellative element is right cancellative. We prove a problem (for finite AG-groupoids) that every left cancellative element of an AG-groupoid (without left identity) is right cancellative. Moreover, we generalize various results of finite AG-groupoids by removing the condition of existence of left identity.
