Geodesic
On congruences of groupoids closely connected with quasigroups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 5, pp. 237-251

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Conditions when a congruence of a left (right) division groupoid and a left (right) cancellation groupoid is closed (“normal”) are given. Conditions for the simplicity of the above-mentioned groupoids are obtained. 
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     title = {On congruences of groupoids closely connected with quasigroups},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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V. A. Shcherbacov; A. Kh. Tabarov; D. I. Puşcaşu. On congruences of groupoids closely connected with quasigroups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 5, pp. 237-251. http://geodesic.mathdoc.fr/item/FPM_2008_14_5_a16/