Geodesic
An equational theory for a~nilpotent $A$-loop
Algebra i logika, Tome 49 (2010) no. 4, pp. 479-497.

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It is shown that a variety generated by a nilpotent $A$-loop has a decidable equational (quasiequational) theory. Thereby the question posed by A. I. Mal'tsev in [Mat. Sb., 69(111), № 1 (1966), 3–12] is answered in the negative, and moreover, a finitely presented nilpotent $A$-loop has a decidable word problem.
Keywords: equational theory, nilpotent $A$-loop, word problem. 
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A. V. Kowalski; V. I. Ursu. An equational theory for a~nilpotent $A$-loop. Algebra i logika, Tome 49 (2010) no. 4, pp. 479-497. http://geodesic.mathdoc.fr/item/AL_2010_49_4_a2/

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