Abstract. Let $L=M(G,2)$ be a $RA2$ loop and $F[L]$ be its loop algebra over a field $F$. In this article, we obtain the unit loop of $F[L]/J(F[L]),$ where $L=M(D_{2p},2)$ is obtained from the dihedral group of order $2p$ ($p$ odd prime), $J(F[L])$ is the Jacobson radical of $F[L]$ and $F$ is a finite field of characteristic $2$. The structure of $1+J(F[L])$ is also determined.
DOI: 10.14232/actasm-015-506-6
AMS Subject Classification
(1991): 20N05, 17D05
Keyword(s):
loop algebra,
Moufang loop,
Zorn's algebra,
general linear loop,
loops $M(G,
2)$
Received February 4, 2014, and in revised form August 27, 2015. (Registered under 6/2015.)
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