On Schur Rings over Cyclic Groups, II Original Research Article

In this paper, we show that for any Schur ringSover a cyclic groupG, if every subgroup is anS-subgroup, thenSis either a wedge product of Schur rings over smaller cyclic groups, or everyS-principal subset is an orbit of an element under a fixed subgroup of AutG. With an earlier result proved by us (on Schur rings over cyclic groups, preprint), we are able to determine all possible structures of Schur rings over a cyclic group.