Schur rings over a Galois ring of odd characteristic

doi:10.1016/j.jcta.2009.12.008

Journal of Combinatorial Theory, Series A

Volume 117, Issue 7, October 2010, Pages 827-841

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Abstract

It is proved that any Schur ring over a Galois ring of odd characteristic is either normal, or of rank 2, or a non-trivial generalized wreath product. The normal Schur rings are characterized as a special subclass of the cyclotomic Schur rings.

Keywords

Schur ring

Galois ring

Normal cyclotomic ring

Generalized wreath product

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¹: The work was partially supported by RFFI Grants 07-01-00485 and 06-01-00471.

²: The work was partially supported by RFFI Grants 07-01-00485, 08-01-00379 and 08-01-00640.