Units in finite loop algebras of RA2 loops

Abstract

Let [Formula: see text] be the loop algebra of a loop [Formula: see text] over a field [Formula: see text]. In this paper, we characterize the structure of the unit loop of [Formula: see text] modulo its Jacobson radical when [Formula: see text] is an [Formula: see text] loop obtained from the dihedral group of order [Formula: see text], [Formula: see text] is an odd number and [Formula: see text] is a finite field of characteristic [Formula: see text]. The structure of [Formula: see text] is also determined.