Geodesic
On Equational Theory of Left Divisible Left Distributive Groupoids
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 51 (2012) no. 2, pp. 67-72.

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It is an open question whether the variety generated by the left divisible left distributive groupoids coincides with the variety generated by the left distributive left quasigroups. In this paper we prove that every left divisible left distributive groupoid with the mapping $a\mapsto a^2$ surjective lies in the variety generated by the left distributive left quasigroups.
Classification : 20N02, 20N05 08B15
Keywords: left distributivity; left idempotency; variety 
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Jedlička, Přemysl. On Equational Theory of Left Divisible Left Distributive Groupoids. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 51 (2012) no. 2, pp. 67-72. http://geodesic.mathdoc.fr/item/AUPO_2012__51_2_a5/