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An equational theory for a nilpotent \(A\)-loop. (English. Russian original) Zbl 1255.20059
Algebra Logic 49, No. 4, 326-339 (2010); translation from Algebra Logika 49, No. 4, 479-497 (2010).
Summary: It is shown that the 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., N. Ser. 69(111), 3-12 (1966; Zbl 0202.31201)] is answered in the negative, and moreover, a finitely presented nilpotent \(A\)-loop has decidable word problem.

MSC:
20N05 Loops, quasigroups
08B05 Equational logic, Mal’tsev conditions
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References:
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