On the separability problem for circulant S-rings

Evdokimov, S.; Ponomarenko, I.

doi:10.1090/spmj/1437

On the separability problem for circulant S-rings
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by S. Evdokimov and I. Ponomarenko

St. Petersburg Math. J. 28 (2017), 21-35

DOI: https://doi.org/10.1090/spmj/1437

Published electronically: November 30, 2016

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Abstract:

A Schur ring (S-ring) over a group $G$ is said to be separable if every of its similarities to another S-ring over $G$ is induced by an isomorphism. A criterion is established for an S-ring to be separable in the case where the group $G$ is cyclic. Using this criterion, it is proved that any S-ring over a cyclic $p$-group is separable and that the class of separable circulant S-rings is closed with respect to duality.

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