Splitting full matrix algebras over algebraic number fields

Let K be a fixed algebraic number field and let A be an associative algebra over K given by structure constants such that A≅Mn(K) holds for some positive integer n. Suppose that n is bounded. Then an isomorphism A→Mn(K) can be constructed by a polynomial time ff-algorithm. An ff-algorithm is a deterministic procedure which is allowed to call oracles for factoring integers and factoring univariate polynomials over finite fields.As a consequence, we obtain a polynomial time ff-algorithm to compute isomorphisms of central simple algebras of bounded degree over K.