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



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Sibirsk. Mat. Zh., 2018, Volume 59, Number 2, Pages 461–467 (Mi smj2986)  

Abelian groups with annihilator ideals of endomorphism rings

A. R. Chekhlov

Tomsk State University, Tomsk, Russia

Abstract: We describe the periodic groups whose endomorphism rings satisfy the annihilator condition for the principal left ideals generated by nilpotent elements. We prove that torsion-free reduced separable, vector, and algebraically compact groups have endomorphism rings with the annihilator condition for the principal left (right) ideals generated by nilpotent elements if and only if these rings are commutative. We show that the almost injective groups (in the sense of Harada) are injective, i.e. divisible.

Keywords: nilpotent endomorphism, annihilator, principal ideal, self-injective endomorphism ring, almost injective group.

DOI: https://doi.org/10.17377/smzh.2018.59.219

Full text: PDF file (271 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2018, 59:2, 363–367

Bibliographic databases:

UDC: 512.541
MSC: 35R30
Received: 15.05.2017

Citation: A. R. Chekhlov, “Abelian groups with annihilator ideals of endomorphism rings”, Sibirsk. Mat. Zh., 59:2 (2018), 461–467; Siberian Math. J., 59:2 (2018), 363–367

Citation in format AMSBIB
\Bibitem{Che18}
\by A.~R.~Chekhlov
\paper Abelian groups with annihilator ideals of endomorphism rings
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 2
\pages 461--467
\mathnet{http://mi.mathnet.ru/smj2986}
\crossref{https://doi.org/10.17377/smzh.2018.59.219}
\elib{http://elibrary.ru/item.asp?id=32817978}
\transl
\jour Siberian Math. J.
\yr 2018
\vol 59
\issue 2
\pages 363--367
\crossref{https://doi.org/10.1134/S0037446618020192}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000430858600019}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85046622466}


Linking options:
  • http://mi.mathnet.ru/eng/smj2986
  • http://mi.mathnet.ru/eng/smj/v59/i2/p461

    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
  • Сибирский математический журнал Siberian Mathematical Journal
    Number of views:
    This page:111
    Full text:13
    References:19
    First page:3

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