On Schur rings over cyclic groups
The notion of Schur ring was first studied by Schur and later by \textit{H. Wielandt} [see his book `Finite permutation groups', Academic Press, New York (1964; Zbl 0138.02501)]. Schur rings have applications in algebraic combinatorics. The aim of this paper is to show that there are simple ways to construct Schur rings over finite cyclic groups from Schur rings over smaller cyclic groups. To this end, the notions of dot product and wedge product on Schur rings are introduced. The second goal is to show that for all except one type of Schur rings over a finite cyclic group \(G\), they can be constructed by using a dot product or wedge product on Schur rings over smaller cyclic groups.
scientific article; zbMATH DE number 1216496