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Normal Subloops in the Integral Loop Ring of an $\RA$ Loop

  Published:2001-03-01
 Printed: Mar 2001
  • Edgar G. Goodaire
  • César Polcino Milies
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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, 17D05, 16S34, 16U60 show english descriptions Loops, quasigroups [See also 05Bxx]
Alternative rings
Group rings [See also 20C05, 20C07], Laurent polynomial rings
Units, groups of units
20N05 - Loops, quasigroups [See also 05Bxx]
17D05 - Alternative rings
16S34 - Group rings [See also 20C05, 20C07], Laurent polynomial rings
16U60 - Units, groups of units
 

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