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., 2016, Volume 21, Issue 2, Pages 184–201 (Mi adm562)  

RESEARCH ARTICLE

Representation of Steinitz's lattice in lattices of substructures of relational structures

Oksana Bezushchaka, Bogdana Oliinykb, Vitaliy Sushchanskyc

a Department of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Volodymyrska, 64, Kyiv 01033, Ukraine
b Department of Mathematics, National University of Kyiv-Mohyla Academy, Skovorody St. 2, Kyiv, 04655, Ukraine
c Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 23, 44-100 Gliwice, Poland

Abstract: General conditions under which certain relational structure contains a lattice of substructures isomorphic to Steinitz's lattice are formulated. Under some natural restrictions we consider relational structures with the lattice containing a sublattice isomorphic to the lattice of positive integers with respect to divisibility. We apply to this sublattice a construction that could be called “lattice completion”. This construction can be used for different types of relational structures, in particular for universal algebras, graphs, metric spaces etc. Some examples are considered.

Keywords: relational structure, lattice, supernatural numbers, Boolean algebra.

Full text: PDF file (372 kB)
References: PDF file   HTML file

Bibliographic databases:
MSC: 03G10, 08A02, 03G05
Received: 11.05.2016
Language:

Citation: Oksana Bezushchak, Bogdana Oliinyk, Vitaliy Sushchansky, “Representation of Steinitz's lattice in lattices of substructures of relational structures”, Algebra Discrete Math., 21:2 (2016), 184–201

Citation in format AMSBIB
\Bibitem{BezOliSus16}
\by Oksana~Bezushchak, Bogdana~Oliinyk, Vitaliy~Sushchansky
\paper Representation of Steinitz's lattice in lattices of~substructures of relational structures
\jour Algebra Discrete Math.
\yr 2016
\vol 21
\issue 2
\pages 184--201
\mathnet{http://mi.mathnet.ru/adm562}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3537445}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000382847700003}


Linking options:
  • http://mi.mathnet.ru/eng/adm562
  • http://mi.mathnet.ru/eng/adm/v21/i2/p184

    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:103
    Full text:41
    References:22

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