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This article is cited in 7 scientific papers (total in 7 papers)
Research Papers
On the separability problem for circulant S-rings
S. Evdokimov, I. Ponomarenko St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka, 27, 191023, St. Petersburg, Russia
Abstract:
A Schur ring (S-ring) over a group $G$ is said to be separable if every of its similaritities 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.
Keywords:
Shur ring, Cayley isomorphism, Cayley graph, circulant S-ring.
Received: 01.06.2015
Citation:
S. Evdokimov, I. Ponomarenko, “On the separability problem for circulant S-rings”, Algebra i Analiz, 28:1 (2016), 32–51; St. Petersburg Math. J., 28:1 (2017), 21–35
Linking options:
https://www.mathnet.ru/eng/aa1478 https://www.mathnet.ru/eng/aa/v28/i1/p32
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Abstract page: | 277 | Full-text PDF : | 49 | References: | 44 | First page: | 15 |
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