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Abstract. 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.

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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.

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