A note on self-dual AG-groupoids | [Journal of Prime Research in Mathematics • 2016]

Author(s):

1. AZIZ-UL-HAKIM: Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan.

2. I. AHMAD: Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan.

3. M. SHAH: Department of Mathematics, Government Post Graduate College Mardan, Pakistan.

Abstract:

In this paper, we enumerate self-dual AG-groupoids up to order 6; and classify them on the basis of commutativity and associativity. A self-dual AG-groupoid-test is introduced to check an arbitrary AG-groupoid for a self-dual AG-groupoid. We also respond to an open problem regarding cancellativity of an element in an AG-groupoid. Some features of ideals in self-dual AG-groupoids are explored. Some desired algebraic structures are constructed from the known ones subject to certain conditions and some subclasses of self-dual AG-groupoids are introduced.

Page(s): 1-15

DOI: DOI not available

Published: Journal: Journal of Prime Research in Mathematics, Volume: 12, Issue: 1, Year: 2016

Keywords:

AGgroupoid , Enumeration , , AMS SUBJECT , connected set , 20N05 , ideal , 20M12 , antirectangular AGgroupoid , Primary 20N02

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