Abel-Grassmann’s Groupoids of Modulo Matrices

  • Aman- ullah Department of Mathematics University of Malakand, Chakdara Dir Lower, Pakistan
  • Muhammad Irshd Department of Mathematics University of Malakand, Chakdara Dir Lower, Pakistan.
  • Imtiaz Ahmad Department of Mathematics University of Malakand, Chakdara Dir Lower, Pakistan.
DOI: https://doi.org/10.22581/muet1982.1601.07

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).

Published
Jan 1, 2016
How to Cite
ULLAH, Aman-; IRSHD, Muhammad; AHMAD, Imtiaz. Abel-Grassmann’s Groupoids of Modulo Matrices. Mehran University Research Journal of Engineering and Technology, [S.l.], v. 35, n. 1, p. 63-70, jan. 2016. ISSN 2413-7219. Available at: <https://publications.muet.edu.pk/index.php/muetrj/article/view/648>. Date accessed: 24 apr. 2024. doi: http://dx.doi.org/10.22581/muet1982.1601.07.
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Issue
Vol 35 No 1 (2016): January Issue
Section
Articles
This is an open Access Article published by Mehran University of Engineering and Technolgy, Jamshoro under CCBY 4.0 International License