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Given a loop l and a ring r, the definition of the loop algebra rl is very similar to the definition of a group algebra. If the characteristic of r is not 2 and the loop algebra rl is alternative, we say that l is an r.A. Loop. We have considered the following problem: given the r.A. Loops l and m and an associative ring r, when will the algebra isomorphism rl'APROXIMADAMENTE IGUAL'rm imply the loop isomorphism l'APROXIMADAMENTE IGUAL'm? we have studied the case when r is a field. First, we consider the case r=q, the rational number field and we study a class of r.A. Loops which is determined by q. Then, we extend this result to fields whose characteristic does not divide the order of the loop