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



Sib. Èlektron. Mat. Izv.:
Year:
Volume:
Issue:
Page:
Find






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


Sib. Èlektron. Mat. Izv., 2015, Volume 12, Pages 232–247 (Mi semr582)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematical logic, algebra and number theory

Planar varieties of semigroups

D. V. Solomatin

Omsk State Pedagogical University, 14, Naberezhnaya Tukhachevskogo, 644099, Omsk, Russia

Abstract: We study the property of planarity of Cayley graphs for varieties of semigroups. It is proved that the variety of semigroups with zero multiplication $\mathrm{ var}\{xy=zt\}$, the variety of left zero semigroups $\mathrm{ var}\{xy=x\}$ and the variety $\mathrm{ var}\{xy=xz\}$ are the only non-trivial planar variety of semigroups. We find the ranks of planarity for some important series of varieties of semigroups.

Keywords: semigroup, Cayley graph, variety of semigroups, planar graph, rank of planarity.

DOI: https://doi.org/10.17377/semi.2015.12.019

Full text: PDF file (3411 kB)
References: PDF file   HTML file

UDC: 512.572
MSC: 20M07
Received December 24, 2014, published April 10, 2015

Citation: D. V. Solomatin, “Planar varieties of semigroups”, Sib. Èlektron. Mat. Izv., 12 (2015), 232–247

Citation in format AMSBIB
\Bibitem{Sol15}
\by D.~V.~Solomatin
\paper Planar varieties of semigroups
\jour Sib. \`Elektron. Mat. Izv.
\yr 2015
\vol 12
\pages 232--247
\mathnet{http://mi.mathnet.ru/semr582}
\crossref{https://doi.org/10.17377/semi.2015.12.019}


Linking options:
  • http://mi.mathnet.ru/eng/semr582
  • http://mi.mathnet.ru/eng/semr/v12/p232

    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. D. V. Solomatin, “Rangi planarnosti mnogoobrazii kommutativnykh polugrupp”, PDM, 2016, no. 4(34), 50–64  mathnet  crossref
  • Number of views:
    This page:307
    Full text:257
    References:400

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