an:06114997
Zbl 1255.20059
Kowalski, A. V.; Ursu, V. I.
An equational theory for a nilpotent \(A\)-loop.
EN
Algebra Logic 49, No. 4, 326-339 (2010); translation from Algebra Logika 49, No. 4, 479-497 (2010).
0002-5232 1573-8302
2010
j
20N05 08B05
equational theories; nilpotent \(A\)-loops; word problem; varieties of loops
Summary: It is shown that the variety generated by a nilpotent \(A\)-loop has a decidable equational (quasiequational) theory. Thereby the question posed by \textit{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.
0202.31201