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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra Logika:
Year:
Volume:
Issue:
Page:
Find






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


Algebra i logika, 2018, Volume 57, Number 5, Pages 522–546
DOI: https://doi.org/10.33048/alglog.2018.57.502
(Mi al864)
 

This article is cited in 1 scientific paper (total in 1 paper)

Nearly finite-dimensional Jordan algebras

V. N. Zhelyabinab, A. S. Panasenkoba

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia
Full-text PDF (244 kB) Citations (1)
References:
Abstract: Nearly finite-dimensional Jordan algebras are examined. Analogs of known results are considered. Namely, it is proved that such algebras are prime and nondegenerate. It is shown that the property of being nearly finite-dimensional is preserved in passing from an alternative algebra to an adjoint Jordan algebra. A similar result is established for associative nearly finite-dimensional algebras with involution. It is stated that a nearly finitedimensional Jordan PI-algebra with unity either is a finite module over a nearly finite-dimensional center or is a central order in an algebra of a nondegenerate symmetric bilinear form. Also the following result holds: if a locally nilpotent ideal has finite codimension in a Jordan algebra with the ascending chain condition on ideals, then that algebra is finite-dimensional. In addition, E. Formanek's result in [Commun. Algebra, 1, No. 1 (1974), 79–86], which says that associative prime PI-rings with unity are embedded in a free module of finite rank over its center, is generalized to Albert rings.
Keywords: nearly finite-dimensional Jordan algebra, associative nearly finite-dimensional algebra with involution, nearly finite-dimensional Jordan PIalgebra with unity, Albert ring.
Funding agency Grant number
Russian Science Foundation 14-21-00065
Supported by Russian Science Foundation, project 14-21-00065.
Received: 22.05.2017
English version:
Algebra and Logic, 2018, Volume 57, Issue 5, Pages 336–352
DOI: https://doi.org/10.1007/s10469-018-9506-5
Bibliographic databases:
Document Type: Article
UDC: 512.554.7
Language: Russian
Citation: V. N. Zhelyabin, A. S. Panasenko, “Nearly finite-dimensional Jordan algebras”, Algebra Logika, 57:5 (2018), 522–546; Algebra and Logic, 57:5 (2018), 336–352
Citation in format AMSBIB
\Bibitem{ZhePan18}
\by V.~N.~Zhelyabin, A.~S.~Panasenko
\paper Nearly finite-dimensional Jordan algebras
\jour Algebra Logika
\yr 2018
\vol 57
\issue 5
\pages 522--546
\mathnet{http://mi.mathnet.ru/al864}
\crossref{https://doi.org/10.33048/alglog.2018.57.502}
\transl
\jour Algebra and Logic
\yr 2018
\vol 57
\issue 5
\pages 336--352
\crossref{https://doi.org/10.1007/s10469-018-9506-5}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000452590800002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85057748269}
Linking options:
  • https://www.mathnet.ru/eng/al864
  • https://www.mathnet.ru/eng/al/v57/i5/p522
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
    Statistics & downloads:
    Abstract page:327
    Full-text PDF :44
    References:44
    First page:6
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024