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Moufang unit loops torsion over their centres
Edgar G. Goodaire, César Polcino Milies
Abstract
Let L be
an RA loop, that is, a loop whose loop ring in any characteristic is an
alternative, but not associative, ring. We find necessary and sufficient
conditions for the (Moufang) unit loop of RL to be
torsion over its centre when R is the ring of rational integers or an arbitrary
field. Over a field, torsion over the centre turns out to be equivalent to
torsion of bounded exponent.
Mathematics Subject Classification
(2000): Primary 20N05; Secondary 16S34, 16U60, 17D05.
Key words: Moufang
loop; alternative ring; loop ring; unit.
Quaestiones
Mathematicae 25 (2002), 1-12.
an RA loop, that is, a loop whose loop ring in any characteristic is an
alternative, but not associative, ring. We find necessary and sufficient
conditions for the (Moufang) unit loop of RL to be
torsion over its centre when R is the ring of rational integers or an arbitrary
field. Over a field, torsion over the centre turns out to be equivalent to
torsion of bounded exponent.
Mathematics Subject Classification
(2000): Primary 20N05; Secondary 16S34, 16U60, 17D05.
Key words: Moufang
loop; alternative ring; loop ring; unit.
Quaestiones
Mathematicae 25 (2002), 1-12.
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Quaestiones Mathematicae. ISSN: 1607-3606