Abel-Grassmann's Groupoids of Modulo Matrices
The binary operation of usual addition is associative in all matrices over R. However, a binary operation of addition in matrices over Z n 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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Mehran University of Engineering and Technology
2016-01-01
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| Series: | Mehran University Research Journal of Engineering and Technology |
| Subjects: | |
| Online Access: | http://publications.muet.edu.pk/research_papers/pdf/pdf1221.pdf |
| Summary: | The binary operation of usual addition is associative in all matrices over R. However, a binary operation of addition in matrices over Z n 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 Z n is transitively commutative AG-groupoid and is a cancellative AG-groupoid ifn is prime. (ii) Every AG-groupoid of matrices over Z n of Type-II is a T3-AG-groupoid. (iii) An AG-groupoid of matrices over Z n ; G nAG(t,u), is an AG-band, ift+ u=1(mod n). |
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| ISSN: | 0254-7821 2413-7219 |