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1. CMB 2015 (vol 58 pp. 363)

Sharma, R. K.; Sidana, Swati
 Finite Semisimple Loop Algebras of Indecomposable $RA$ Loops There are at the most seven classes of finite indecomposable $RA$ loops upto isomorphism. In this paper, we completely characterize the structure of the unit loop of loop algebras of these seven classes of loops over finite fields of characteristic greater than $2$. Keywords:unit loop, loop algebra, indecomposable $RA$ loopsCategories:20N05, 17D05

2. CMB 2009 (vol 52 pp. 245)

Goodaire, Edgar G.; Milies, César Polcino
 Involutions of RA Loops Let $L$ be an RA loop, that is, a loop whose loop ring over any coefficient ring $R$ is an alternative, but not associative, ring. Let $\ell\mapsto\ell^\theta$ denote an involution on $L$ and extend it linearly to the loop ring $RL$. An element $\alpha\in RL$ is \emph{symmetric} if $\alpha^\theta=\alpha$ and \emph{skew-symmetric} if $\alpha^\theta=-\alpha$. In this paper, we show that there exists an involution making the symmetric elements of $RL$ commute if and only if the characteristic of $R$ is $2$ or $\theta$ is the canonical involution on $L$, and an involution making the skew-symmetric elements of $RL$ commute if and only if the characteristic of $R$ is $2$ or $4$. Categories:20N05, 17D05

3. CMB 2001 (vol 44 pp. 27)

Goodaire, Edgar G.; Milies, César Polcino
 Normal Subloops in the Integral Loop Ring of an $\RA$ Loop 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. Categories:20N05, 17D05, 16S34, 16U60
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