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.)