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), No 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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     author = {A. V. Kowalski and V. I. Ursu},
     title = {An equational theory for a~nilpotent $A$-loop},
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     pages = {479--497},
     publisher = {mathdoc},
     volume = {49},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2010_49_4_a2/}
}
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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/