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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Fundam. Prikl. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Fundam. Prikl. Mat., 2007, Volume 13, Issue 5, Pages 193–200 (Mi fpm1080)  

This article is cited in 6 scientific papers (total in 6 papers)

Rings over which all modules are $I_0$-modules

A. A. Tuganbaev

Russian State University of Trade and Economics

Abstract: Let $A$ be a ring that does not contain an infinite set of idempotents that are orthogonal modulo the ideal $\operatorname{SI}(A_A)$. It is proved that all $A$-modules are $I_0$-modules if and only if either $A$ is a right semi-Artinian right V-ring or $A/\operatorname{SI}(A_A)$ is an Artinian serial ring and the square of the Jacobson radical of $A/\operatorname{SI}(A_A)$ is equal to zero.

Full text: PDF file (122 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2009, 156:2, 336–341

Bibliographic databases:

UDC: 512.55

Citation: A. A. Tuganbaev, “Rings over which all modules are $I_0$-modules”, Fundam. Prikl. Mat., 13:5 (2007), 193–200; J. Math. Sci., 156:2 (2009), 336–341

Citation in format AMSBIB
\Bibitem{Tug07}
\by A.~A.~Tuganbaev
\paper Rings over which all modules are $I_0$-modules
\jour Fundam. Prikl. Mat.
\yr 2007
\vol 13
\issue 5
\pages 193--200
\mathnet{http://mi.mathnet.ru/fpm1080}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2379746}
\zmath{https://zbmath.org/?q=an:1182.16002}
\transl
\jour J. Math. Sci.
\yr 2009
\vol 156
\issue 2
\pages 336--341
\crossref{https://doi.org/10.1007/s10958-008-9270-5}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-58149516317}


Linking options:
  • http://mi.mathnet.ru/eng/fpm1080
  • http://mi.mathnet.ru/eng/fpm/v13/i5/p193

    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
    Cycle of papers

    This publication is cited in the following articles:
    1. A. N. Abyzov, A. A. Tuganbaev, “Rings over which all modules are $I_0$-modules. II”, J. Math. Sci., 162:5 (2009), 587–593  mathnet  crossref  mathscinet  zmath
    2. A. A. Tuganbaev, “Rings without infinite sets of noncentral orthogonal idempotents”, J. Math. Sci., 162:5 (2009), 730–739  mathnet  crossref  mathscinet  zmath
    3. A. N. Abyzov, A. A. Tuganbaev, “Submodules and direct summands”, J. Math. Sci., 164:1 (2010), 1–20  mathnet  crossref  mathscinet
    4. A. N. Abyzov, “Generalized $SV$-rings of bounded index of nilpotency”, Russian Math. (Iz. VUZ), 55:12 (2011), 1–10  mathnet  crossref  mathscinet
    5. A. N. Abyzov, “On some classes of semiartinian rings”, Siberian Math. J., 53:5 (2012), 763–771  mathnet  crossref  mathscinet  isi
    6. A. N. Abyzov, “$I_0^*$-modules”, Russian Math. (Iz. VUZ), 58:8 (2014), 1–14  mathnet  crossref
  • Фундаментальная и прикладная математика
    Number of views:
    This page:247
    Full text:83
    References:44
    First page:1

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