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



Bul. Acad. Ştiinţe Repub. Mold. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Bul. Acad. Ştiinţe Repub. Mold. Mat., 2011, Number 1, Pages 3–27 (Mi basm275)  

Survey articles

Serial rings and their generalizations

Vladimir Kirichenko, Makar Plakhotnyk

Mech-Math. Dept., Kyiv Taras Shevchenko Univ., Kyiv, Ukraine

Abstract: We give a survey of results on the theory of semiprime semidistributive rings, in particular, serial rings. Besides this we prove that a serial ring is Artinian if and only if some power of its Jacobson radical is zero. Also we prove that a serial ring is Noetherian if and only if the intersection of all powers of Jacobson radical is zero. These two theorems hold for semiperfect semidistributive rings.

Keywords and phrases: serial ring, SPSD-ring, quiver of ring.

Full text: PDF file (296 kB)
References: PDF file   HTML file

Bibliographic databases:
MSC: 16L30
Received: 06.12.2010
Language:

Citation: Vladimir Kirichenko, Makar Plakhotnyk, “Serial rings and their generalizations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2011, no. 1, 3–27

Citation in format AMSBIB
\Bibitem{KirPla11}
\by Vladimir~Kirichenko, Makar~Plakhotnyk
\paper Serial rings and their generalizations
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2011
\issue 1
\pages 3--27
\mathnet{http://mi.mathnet.ru/basm275}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2849224}
\zmath{https://zbmath.org/?q=an:1235.16018}


Linking options:
  • http://mi.mathnet.ru/eng/basm275
  • http://mi.mathnet.ru/eng/basm/y2011/i1/p3

    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
  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
    Number of views:
    This page:280
    Full text:89
    References:43
    First page:1

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