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Finite AG-groupoid with left identity and left zero

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  • Qaiser Mushtaq
  • M. S. Kamran

Abstract

A groupoid G whose elements satisfy the left invertive law: ( a b ) c = ( c b ) 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.

Suggested Citation

  • Qaiser Mushtaq & M. S. Kamran, 2001. "Finite AG-groupoid with left identity and left zero," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 27, pages 1-3, January.
    • Handle: RePEc:hin:jijmms:620512
    DOI: 10.1155/S0161171201010997
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    Cited by:

    1. Xiaoying Wu & Xiaohong Zhang, 2019. "The Decomposition Theorems of AG-Neutrosophic Extended Triplet Loops and Strong AG-( l , l )-Loops," Mathematics, MDPI, vol. 7(3), pages 1-13, March.

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