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 Discrete Math.:
Year:
Volume:
Issue:
Page:
Find






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


Algebra Discrete Math., 2018, Volume 26, Issue 1, Pages 47–64 (Mi adm669)  

RESEARCH ARTICLE

Module decompositions via Rickart modules

A. Harmancia, B. Ungorb

a Department of Mathematics, Hacettepe University, Turkey
b Department of Mathematics, Ankara University, Turkey

Abstract: This work is devoted to the investigation of module decompositions which arise from Rickart modules, socle and radical of modules. In this regard, the structure and several illustrative examples of inverse split modules relative to the socle and radical are given. It is shown that a module $M$ has decompositions $M=\operatorname{Soc}(M) \oplus N$ and $M=\operatorname{Rad}(M) \oplus K$ where $N$ and $K$ are Rickart if and only if $M$ is $\operatorname{Soc}(M)$-inverse split and $\operatorname{Rad}(M)$-inverse split, respectively. Right $\operatorname{Soc}( \cdot )$-inverse split left perfect rings and semiprimitive right hereditary rings are determined exactly. Also, some characterizations for a ring $R$ which has a decomposition $R=\operatorname{Soc}(R_R)\oplus I$ with $I$ a hereditary Rickart module are obtained.

Keywords: $\operatorname{Soc}( \cdot )$-inverse split module, $\operatorname{Rad}( \cdot )$-inverse split module, Rickart module.

Full text: PDF file (389 kB)
References: PDF file   HTML file
MSC: 16D10, 16D40, 16D80
Received: 22.10.2016
Revised: 15.12.2017
Language:

Citation: A. Harmanci, B. Ungor, “Module decompositions via Rickart modules”, Algebra Discrete Math., 26:1 (2018), 47–64

Citation in format AMSBIB
\Bibitem{HarUng18}
\by A.~Harmanci, B.~Ungor
\paper Module decompositions via Rickart modules
\jour Algebra Discrete Math.
\yr 2018
\vol 26
\issue 1
\pages 47--64
\mathnet{http://mi.mathnet.ru/adm669}


Linking options:
  • http://mi.mathnet.ru/eng/adm669
  • http://mi.mathnet.ru/eng/adm/v26/i1/p47

    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
  • Algebra and Discrete Mathematics
    Number of views:
    This page:26
    Full text:13
    References:11

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