Schur rings over a product of Galois rings
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry - Tập 55 - Trang 105-138 - 2013
Tóm tắt
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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