Normal Subloops in the Integral Loop Ring of an $\RA$ Loop
Printed: Mar 2001
Edgar G. Goodaire
César Polcino Milies
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.
20N05 - Loops, quasigroups [See also 05Bxx]
17D05 - Alternative rings
16S34 - Group rings [See also 20C05, 20C07], Laurent polynomial rings
16U60 - Units, groups of units