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Abel-Grassmann`s groupoids of modulo matrices.

Author(s)
Amanullah Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Pakistan
Muhammad Rashad Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Pakistan
Imtiaz Ahmad Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Pakistan
Abstract
The binary operation of usual addition is associative in all matrices over R. However, a binary operation of addition in matrices over Zn of a nonassociative structures of AG-groupoids and AG-groups are defined and investigated here. It is shown that both these structures exist for every integer n > 3. Various properties of these structures are explored like: (i) Every AG-groupoid of matrices over Zn is transitively commutative AG-groupoid and is a cancellative AG-groupoid if n is prime. (ii) Every AG-groupoid of matrices over Zn of Type-II is a T3-AG-groupoid. (iii) An AG-groupoid of matrices over Zn; GnAG(t,u), is an AG-band, if t+ u=1(mod n).
Publication Details
Page(s) 63-70
DOI DOI not available
Published Journal: Mehran University Research Journal of Engineering and Technology, Volume: 35, Issue: 1, Year: 2016

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