Abel-Grassmann`s groupoids of modulo matrices. | [Mehran University Research Journal of Engineering and Technology • 2016]

Author(s):

1. Amanullah : Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Pakistan

2. Muhammad Rashad: Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Pakistan

3. 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).

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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