Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

Request Permissions   Purchase Content 
 

 

On the separability problem for circulant S-rings


Authors: S. Evdokimov and I. Ponomarenko
Original publication: Algebra i Analiz, tom 28 (2016), nomer 1.
Journal: St. Petersburg Math. J. 28 (2017), 21-35
MSC (2010): Primary 20B25
DOI: https://doi.org/10.1090/spmj/1437
Published electronically: November 30, 2016
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 20B25

Retrieve articles in all journals with MSC (2010): 20B25


Additional Information

S. Evdokimov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
Email: evdokim@pdmi.ras.ru

I. Ponomarenko
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
Email: inp@pdmi.ras.ru

DOI: https://doi.org/10.1090/spmj/1437
Keywords: Shur ring, Cayley isomorphism, Cayley graph, circulant S-ring
Received by editor(s): June 1, 2015
Published electronically: November 30, 2016
Additional Notes: The second author was partially supported by RFBR (grant no. 14-01-00156)
Article copyright: © Copyright 2016 American Mathematical Society