Schur Rings over Z \times Z_3

TL;DR

This paper classifies all Schur rings over the group Z x Z_3, demonstrating that they are all of a traditional type, thus providing a complete structural understanding of these algebraic objects.

Contribution

The paper provides a complete classification of Schur rings over Z x Z_3, showing they are all traditional, which was previously unknown.

Findings

All Schur rings over Z x Z_3 are traditional.

The classification provides a complete structural understanding.

The result extends the theory of Schur rings over infinite cyclic groups.

Abstract

For the direct product $\cZ\times \cZ_3$ of infinite cyclic group $\cZ$ and a cyclic group $\cZ_3$ of order $3$, the schur rings over it are classified. In particular, all the schur rings are proved to be traditional.