On wreath products of C-algebras, table algebras, and association schemes

In this paper we will first present characterizations of wreath products of C-algebras, and show that the dual of the wreath product of C-algebras is isomorphic to the wreath product of the duals of those C-algebras in the reverse order. Then we prove the Krull–Schmidt type theorems for the wreath products of table algebras as well as for the wreath products of association schemes.