A. V. Kowalski, V. I. Ursu, “An equational theory for a nilpotent <nobr>$A$</nobr>-loop”, Algebra Logika, 2010, Volume 49, Number 4,Pages <nobr>479

This article is cited in 2 papers

An equational theory for a nilpotent $A$-loop

A. V. Kowalski^a, V. I. Ursu^bc

^a Creanga State Pedagogical University, Chisinau, Republic of Moldova
^b Technical University of Moldova, Chisinau, Republic of Moldova
^c Institute of Mathematics of the Romanian Academy, Bucharest, Romania

Abstract: 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.

UDC: 512.548.77+512.572

Received: 09.11.2009