arXiv subjects
Publications and source records attributed to Zhiman Wu.
Schur rings are a type of subrings of group rings afforded by a partition of the underlined group. In this paper, Schur rings over free abelian group of rank two are classified under the assumption that one of the direct factor is a union of some basic sets. There are eight different types, and all but one type of which are traditional.
Schur rings over the infinite dihedral group $\mathcal{Z}\rtimes\mathcal{Z}_2$ are studied according to properties of Schur rings over infinite groups and the classification of Schur rings over infinite cyclic groups. Schur rings over $\mathcal{Z}\rtimes{\mathcal{Z}}_2$ are classified under the assumption that $\mathcal{Z}$ is an $\mathcal{A}$-subgroup. Those Schur rings are proved to be traditional.