RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 4 scientific papers (total in 4 papers)

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.

Full text: PDF file (378 kB)
References: PDF file   HTML file

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

Bibliographic databases:

MSC: 13M99
Received: 30.07.2007

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}


Linking options:
  • http://mi.mathnet.ru/eng/aa146
  • http://mi.mathnet.ru/eng/aa/v19/i6/p59

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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  crossref  mathscinet  zmath  isi  elib  scopus
    2. Muzychuk M., Ponomarenko I., “Schur rings”, European J. Combin., 30:6 (2009), 1526–1539  crossref  mathscinet  zmath  isi  elib  scopus
    3. Evdokimov S., Ponomarenko I., “Schur rings over a Galois ring of odd characteristic”, J. Combin. Theory Ser. A, 117:7 (2010), 827–841  crossref  mathscinet  zmath  isi  elib  scopus
    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  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и анализ St. Petersburg Mathematical Journal
    Number of views:
    This page:225
    Full text:65
    References:28
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020