Matematicheskie Zametki
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, 1973, Volume 14, Issue 5, Pages 703–712 (Mi mz9955)  

This article is cited in 2 scientific papers (total in 2 papers)

Nilpotent shifts on manifolds

I. I. Mel'nik

Saratov State University

Abstract: On the lattice of manifolds of all algebras $L$ we study the operator of nilpotent closure $J:\alpha\to\alpha+\mathfrak{R}$, where $\mathfrak{R}$ is a nilpotent manifold of $\Omega$-algebras. With a given system of identities $\Sigma$ defining $\alpha$, we construct a system $\Sigma^*$, giving the manifold $\alpha+\mathfrak{R}$. It is proved that if $\alpha$ does not contain $\mathfrak{R}$, then the lattice of submanifolds of $\alpha+\mathfrak{R}$ is the double of the lattice of submanifolds of $\alpha$. We describe the free and subdirect indecomposable manifolds of algebras $\alpha+\mathfrak{R}$. Let $B\in\alpha+\mathfrak{R}$ and $A$ be a dense retract of $B$. We denote by $\theta(B)$ the lattice of congruences on $B$. The theorem is proved: $\theta(B)$ is a complemented lattice if and only if $\theta(A)$ is a complemented lattice.

Full text: PDF file (1511 kB)

English version:
Mathematical Notes, 1973, 14:5, 962–966

Bibliographic databases:

UDC: 512
Received: 12.07.1972

Citation: I. I. Mel'nik, “Nilpotent shifts on manifolds”, Mat. Zametki, 14:5 (1973), 703–712; Math. Notes, 14:5 (1973), 962–966

Citation in format AMSBIB
\Bibitem{Mel73}
\by I.~I.~Mel'nik
\paper Nilpotent shifts on manifolds
\jour Mat. Zametki
\yr 1973
\vol 14
\issue 5
\pages 703--712
\mathnet{http://mi.mathnet.ru/mz9955}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=366782}
\zmath{https://zbmath.org/?q=an:0285.08002}
\transl
\jour Math. Notes
\yr 1973
\vol 14
\issue 5
\pages 962--966
\crossref{https://doi.org/10.1007/BF01462258}


Linking options:
  • http://mi.mathnet.ru/eng/mz9955
  • http://mi.mathnet.ru/eng/mz/v14/i5/p703

    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. Davidova D.S. Movsisyan Yu.M., “Hyperidentities of Weakly Idempotent Lattices”, J. Contemp. Math. Anal.-Armen. Aca., 50:6 (2015), 259–264  crossref  isi
    2. Movsisyan Yu., Davidova D., “a Complete Characterization of Hyperidentities of the Variety of Weakly Idempotent Lattices”, Tenth International Conference on Computer Science and Information Technologies Revised Selected Papers Csit-2015, ed. Shoukourian S., IEEE, 2015, 41–43  mathscinet  isi
  • Математические заметки Mathematical Notes
    Number of views:
    This page:76
    Full text:43
    First page:1

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021