Ring Isomorphism of Cyclic Cyclotomic Algebras

It is shown that ring isomorphisms between cyclic cyclotomic algebras over cyclotomic number fields are essentially determined by the list of local Schur indices at all rational primes. As a consequence, ring isomorphisms between simple components of the rational group algebras of finite metacyclic groups are determined by the center, the dimension over ?, and the list of local Schur indices at rational primes. An example is given to show that this does not hold for finite groups in general.