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 Algebra i Analiz: Year: Volume: Issue: Page: Find

 Algebra i Analiz, 2007, Volume 19, Issue 6, Pages 59–85 (Mi aa146)

Research Papers

Normal cyclotomic schemes over a finite commutative ring

S. A. Evdokimov, I. N. Ponomarenko

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: Cyclotomic association schemes over a finite commutative ring $R$ with identity are studied. The main goal is to identify the normal cyclotomic schemes $\mathcal{C}$, i.e., those for which $\operatorname{Aut}(\mathcal{C})\le A\Gamma L_1(R)$. The problem reduces to the case where the ring $R$ is local, and in this case a necessary condition of normality in terms of the subgroup of $R^\times$ that determines $\mathcal{C}$ is given. This condition is proved to be sufficient for a large class of local rings including the Galois rings of odd characteristic.

Keywords: Association scheme, cyclotomic schemes.

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English version:
St. Petersburg Mathematical Journal, 2008, 19:6, 911–929

Bibliographic databases:

MSC: 13M99

Citation: S. A. Evdokimov, I. N. Ponomarenko, “Normal cyclotomic schemes over a finite commutative ring”, Algebra i Analiz, 19:6 (2007), 59–85; St. Petersburg Math. J., 19:6 (2008), 911–929

Citation in format AMSBIB
\Bibitem{EvdPon07} \by S.~A.~Evdokimov, I.~N.~Ponomarenko \paper Normal cyclotomic schemes over a finite commutative ring \jour Algebra i Analiz \yr 2007 \vol 19 \issue 6 \pages 59--85 \mathnet{http://mi.mathnet.ru/aa146} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2411639} \zmath{https://zbmath.org/?q=an:1206.13029} \transl \jour St. Petersburg Math. J. \yr 2008 \vol 19 \issue 6 \pages 911--929 \crossref{https://doi.org/10.1090/S1061-0022-08-01027-3} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000267497100003} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Evdokimov S., Ponomarenko I., “Permutation group approach to association schemes”, European J. Combin., 30:6 (2009), 1456–1476
2. Muzychuk M., Ponomarenko I., “Schur rings”, European J. Combin., 30:6 (2009), 1526–1539
3. Evdokimov S., Ponomarenko I., “Schur rings over a Galois ring of odd characteristic”, J. Combin. Theory Ser. A, 117:7 (2010), 827–841
4. Ikuta T., Munemasa A., “Butson-Type Complex Hadamard Matrices and Association Schemes on Galois Rings of Characteristic 4”, Spec. Matrices, 6:1 (2018), 1–10
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