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Normal Subloops in the Integral Loop Ring of an $\RA$ Loop |
Canad. Math. Bull. 44(2001), 27-35
Published:2001-03-01
Printed: Mar 2001
Printed: Mar 2001
- Edgar G. Goodaire
- César Polcino Milies
Abstract
We show that an $\RA$ loop has a torsion-free normal complement in the
loop of normalized units of its integral loop ring. We also
investigate whether an $\RA$ loop can be normal in its unit loop.
Over fields, this can never happen.
| MSC Classifications: |
20N05 - Loops, quasigroups [See also 05Bxx] 17D05 - Alternative rings 16S34 - Group rings [See also 20C05, 20C07], Laurent polynomial rings 16U60 - Units, groups of units |