RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2018, Volume 104, Issue 2, Pages 309–317 (Mi mz11711)  

Sequences of Endomorphism Groups of Abelian Groups

E. A. Timoshenkoa, A. V. Tsarevb

a Tomsk State University
b Moscow State Pedagogical University

Abstract: In the paper, Problem 18.3 of the book “Abelian groups” (2015) by L. Fuchs is solved in the case of Abelian groups with finite $p$-ranks. For an Abelian group $A$, a sequence of groups $(A_n)$ is considered, where $A_0=A$ and $A_{n+1}=\operatorname{End}A_n$. It is shown that, if all $p$-ranks of the group $A$ are finite, then this sequence can stabilize either after $A_0$ or after $A_1$.

Keywords: Abelian group, $E$-ring, $E$-group, $p$-rank.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.12877.2018/12.1

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm11711

Full text: PDF file (499 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Mathematical Notes, 2018, 104:2, 309–315

Bibliographic databases:

UDC: 512.541
Received: 01.06.2017

Citation: E. A. Timoshenko, A. V. Tsarev, “Sequences of Endomorphism Groups of Abelian Groups”, Mat. Zametki, 104:2 (2018), 309–317; Math. Notes, 104:2 (2018), 309–315

Citation in format AMSBIB
\Bibitem{TimTsa18}
\by E.~A.~Timoshenko, A.~V.~Tsarev
\paper Sequences of Endomorphism Groups of Abelian Groups
\jour Mat. Zametki
\yr 2018
\vol 104
\issue 2
\pages 309--317
\mathnet{http://mi.mathnet.ru/mz11711}
\crossref{https://doi.org/10.4213/mzm11711}
\elib{http://elibrary.ru/item.asp?id=35410191}
\transl
\jour Math. Notes
\yr 2018
\vol 104
\issue 2
\pages 309--315
\crossref{https://doi.org/10.1134/S0001434618070325}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000446511500032}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85054497032}


Linking options:
  • http://mi.mathnet.ru/eng/mz11711
  • https://doi.org/10.4213/mzm11711
  • http://mi.mathnet.ru/eng/mz/v104/i2/p309

    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
  • Математические заметки Mathematical Notes
    Number of views:
    This page:151
    References:23
    First page:22

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