Schur rings over a product of Galois rings

Details Schur rings over a product of Galois rings Schur rings over a product of Galois rings

2009-12-08

arxiv.org/abs/0912.1559v2

Mathematics

Combinatorics

minor improvements

Scientific paper

The recently developed theory of Schur rings over a finite cyclic group is generalized to Schur rings over a ring R being a product of Galois rings of coprime characteristics. It is proved that if the characteristic of R is odd, then as in the cyclic group case any pure Schur ring over R is the tensor product of a pure cyclotomic ring and Schur rings of rank 2 over non-fields. Moreover, it is shown that in contrast to the cyclic group case there are non-pure Schur rings over R that are not generalized wreath products.

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