Finite AG-groupoid with left identity and left zero
A groupoid G whose elements satisfy the left invertive law: (ab)c=(cb)a is known as Abel-Grassman's groupoid (AG-groupoid). It is a nonassociative algebraic structure midway between a groupoid and a commutative semigroup. In this note, we show that if G is a finite AG-groupoid with a left zero...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201010997 |
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| _version_ | 1832549407254380544 |
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| author | Qaiser Mushtaq M. S. Kamran |
| author_facet | Qaiser Mushtaq M. S. Kamran |
| author_sort | Qaiser Mushtaq |
| collection | DOAJ |
| description | A groupoid G whose elements satisfy the left invertive law:
(ab)c=(cb)a is known as Abel-Grassman's groupoid (AG-groupoid).
It is a nonassociative algebraic structure midway between a
groupoid and a commutative semigroup. In this note, we show that
if G is a finite AG-groupoid with a left zero then, under
certain conditions, G without the left zero element is a commutative group. |
| format | Article |
| id | doaj-art-d578c94fe9f4498ca59737e6e1a2ec69 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d578c94fe9f4498ca59737e6e1a2ec692025-02-03T06:11:21ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0127638738910.1155/S0161171201010997Finite AG-groupoid with left identity and left zeroQaiser Mushtaq0M. S. Kamran1Department of Mathematics, Quaid-i-Azam University, Islamabad, PakistanDepartment of Mathematics, Quaid-i-Azam University, Islamabad, PakistanA groupoid G whose elements satisfy the left invertive law: (ab)c=(cb)a is known as Abel-Grassman's groupoid (AG-groupoid). It is a nonassociative algebraic structure midway between a groupoid and a commutative semigroup. In this note, we show that if G is a finite AG-groupoid with a left zero then, under certain conditions, G without the left zero element is a commutative group.http://dx.doi.org/10.1155/S0161171201010997 |
| spellingShingle | Qaiser Mushtaq M. S. Kamran Finite AG-groupoid with left identity and left zero International Journal of Mathematics and Mathematical Sciences |
| title | Finite AG-groupoid with left identity and left zero |
| title_full | Finite AG-groupoid with left identity and left zero |
| title_fullStr | Finite AG-groupoid with left identity and left zero |
| title_full_unstemmed | Finite AG-groupoid with left identity and left zero |
| title_short | Finite AG-groupoid with left identity and left zero |
| title_sort | finite ag groupoid with left identity and left zero |
| url | http://dx.doi.org/10.1155/S0161171201010997 |
| work_keys_str_mv | AT qaisermushtaq finiteaggroupoidwithleftidentityandleftzero AT mskamran finiteaggroupoidwithleftidentityandleftzero |