On the structure of basic sets of Schur rings over cyclic groups (Q1337446)

The author proves the following conjecture of M. Klin: Two Schur rings defined over the same cyclic group are isomorphic iff they coincide. (Here the definition of isomorphism involves the preservation of the Hadamard product \((\sum x_ g g) \circ (\sum y_ g g) = \sum(x_ g y_ g)g\) and the involution \(\sum x_ g g \mapsto \sum x_ g g^{-1}\) as well.) The main tool in the sophisticated proof is a useful description of basic sets with a trivial radical.