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, 1968, Volume 4, Issue 6, Pages 639–648 (Mi mz6784)  

This article is cited in 5 scientific papers (total in 5 papers)

The theory of radicals in lattice-ordered rings

M. A. Shatalova

All-Union Correspondence Machine-Building Institute

Abstract: Special classes of associative lattice-ordered rings are introduced which are analogous to V. A. Andrunakievich's special classes of rings. The appropriate special radicals for them are defined. It is shown that the special classes of $l$-rings are: 1) the class of all $l$-primary $l$-rings; 2) the class of all $l$-primary $l$-rings without locally nilpotent $l$-ideals (it is shown that the corresponding $l$-ideal is a union of nil-$l$-ideals of the ring); 3) the class of $l$-rings not containing strictly positive divisors of zero; 4) the class of subdirectly indecomposable $l$-rings with $l$-idempotent core.

Full text: PDF file (943 kB)

English version:
Mathematical Notes, 1968, 4:6, 875–880

Bibliographic databases:

UDC: 512.4
Received: 27.02.1968

Citation: M. A. Shatalova, “The theory of radicals in lattice-ordered rings”, Mat. Zametki, 4:6 (1968), 639–648; Math. Notes, 4:6 (1968), 875–880

Citation in format AMSBIB
\Bibitem{Sha68}
\by M.~A.~Shatalova
\paper The theory of radicals in lattice-ordered rings
\jour Mat. Zametki
\yr 1968
\vol 4
\issue 6
\pages 639--648
\mathnet{http://mi.mathnet.ru/mz6784}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=253960}
\zmath{https://zbmath.org/?q=an:0195.32707|0165.35404}
\transl
\jour Math. Notes
\yr 1968
\vol 4
\issue 6
\pages 875--880
\crossref{https://doi.org/10.1007/BF01110821}


Linking options:
  • http://mi.mathnet.ru/eng/mz6784
  • http://mi.mathnet.ru/eng/mz/v4/i6/p639

    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

    This publication is cited in the following articles:
    1. N. E. Shavgulidze, “Radicals of $l$-rings and one-sided $l$-ideals”, J. Math. Sci., 166:5 (2010), 682–690  mathnet  crossref  mathscinet
    2. N. E. Shavgulidze, “Special classes of $l$-rings”, J. Math. Sci., 166:6 (2010), 794–805  mathnet  crossref  mathscinet  elib
    3. N. E. Shavgulidze, “Radicals and $l$-modules”, J. Math. Sci., 169:5 (2010), 717–723  mathnet  crossref  mathscinet
    4. J. V. Kochetova, E. E. Shirshova, “Prime radicals of lattice $\mathcal K$-ordered algebras”, J. Math. Sci., 201:4 (2014), 465–518  mathnet  crossref  mathscinet
    5. B. J. Gardner, “Later developments based on some ideas of Andrunachievici: Special radicals and The Lemma”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, no. 2, 113–137  mathnet
  • Математические заметки Mathematical Notes
    Number of views:
    This page:165
    Full text:48
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019