Geodesic
On ordered Abel--Grassmann’s groupoids
Problemy fiziki, matematiki i tehniki, no. 2 (2015), pp. 40-47

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The concept of $(m,n)$-ideals in ordered $\mathcal{AG}$-groupoids is introduced and the $(0,2)$-ideals and $(1,2)$-ideals of an ordered $\mathcal{AG}$-groupoid in terms of left ideals are characterised. It is shown that an ordered $\mathcal{AG}$-groupoid $S$ is $0$–$(0,2)$-bisimple if and only if $S$ is right $0$-simple. The results of this paper extend the concept of an $\mathcal{AG}$-groupoid without order. Finally, we characterize an intra-regular ordered $\mathcal{AG}$-groupoid in terms of left and right ideals.
Keywords: ordered $\mathcal{AG}$-groupoids, left invertive law, left identity, $(m,n)$-ideals. 
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     author = {Waqar Khan and Faisal Yousafzai and Asad Khan},
     title = {On ordered {Abel--Grassmann{\textquoteright}s} groupoids},
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     pages = {40--47},
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     number = {2},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2015_2_a5/}
}
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Waqar Khan; Faisal Yousafzai; Asad Khan. On ordered Abel--Grassmann’s groupoids. Problemy fiziki, matematiki i tehniki, no. 2 (2015), pp. 40-47. http://geodesic.mathdoc.fr/item/PFMT_2015_2_a5/