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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Diskr. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Diskr. Mat., 2010, Volume 22, Issue 2, Pages 148–159 (Mi dm1101)  

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

On the potential divisibility of matrices over distributive lattices

I. B. Kozhukhov, V. A. Yaroshevich


Abstract: We consider matrices of arbitrary sizes (including infinite matrices) over a distributive lattice $L$ and prove that if $L=2^X$ is a lattice of all subsets of a set $X$, then the potential divisibility of matrices (from the left or from the right) of one of the matrices by the other matrix is equivalent to the usual divisibility. In particular, in the semigroup of square matrices over the lattice $2^X$ the Green relation $\mathscr L$ coincides with the generalised Green relation $\mathscr L^*$.

DOI: https://doi.org/10.4213/dm1101

Full text: PDF file (159 kB)
References: PDF file   HTML file

English version:
Discrete Mathematics and Applications, 2010, 20:3, 291–305

Bibliographic databases:

UDC: 512.533
Received: 01.06.2009

Citation: I. B. Kozhukhov, V. A. Yaroshevich, “On the potential divisibility of matrices over distributive lattices”, Diskr. Mat., 22:2 (2010), 148–159; Discrete Math. Appl., 20:3 (2010), 291–305

Citation in format AMSBIB
\Bibitem{KozYar10}
\by I.~B.~Kozhukhov, V.~A.~Yaroshevich
\paper On the potential divisibility of matrices over distributive lattices
\jour Diskr. Mat.
\yr 2010
\vol 22
\issue 2
\pages 148--159
\mathnet{http://mi.mathnet.ru/dm1101}
\crossref{https://doi.org/10.4213/dm1101}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2730134}
\zmath{https://zbmath.org/?q=an:05773261}
\elib{http://elibrary.ru/item.asp?id=20730341}
\transl
\jour Discrete Math. Appl.
\yr 2010
\vol 20
\issue 3
\pages 291--305
\crossref{https://doi.org/10.1515/DMA.2010.017}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77954717323}


Linking options:
  • http://mi.mathnet.ru/eng/dm1101
  • https://doi.org/10.4213/dm1101
  • http://mi.mathnet.ru/eng/dm/v22/i2/p148

    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. Yu. I. Kozhukhova, “Potentsialno prostye sprava konechnye polugruppy”, Chebyshevskii sb., 12:1 (2011), 120–123  mathnet  mathscinet
    2. Amerbaev V.M., Kozhukhov I.B., Revyakin A.M., “Predstavleniya binarnykh otnoshenii v teorii izmerenii i poleznosti dlya otsenki sotsialnogo kapitala”, Vestnik Moskovskoi gosudarstvennoi akademii delovogo administrirovaniya. Ser. Ekonomika, 2012, no. 4, 66–71  elib
  • Дискретная математика
    Number of views:
    This page:377
    Full text:112
    References:33
    First page:29

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