Prikladnaya Diskretnaya Matematika
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



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






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


Prikladnaya Diskretnaya Matematika, 2016, Number 4(34), Pages 50–64
DOI: https://doi.org/10.17223/20710410/34/4
(Mi pdm567)
 

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

Theoretical Backgrounds of Applied Discrete Mathematics

The ranks of planarity for varieties of commutative semigroups

D. V. Solomatin

Omsk State Pedagogical University, Omsk, Russia
References:
Abstract: We study the concept of the planarity rank suggested by L. M. Martynov for semigroup varieties. Let $V$ be a variety of semigroups. If there is a natural number $r\geq 1$ that all $V$-free semigroups of ranks $\leq r$ allow planar Cayley graphs and the $V$-free semigroup of a rank $r+1$ doesn't allow planar Cayley graph, then this number $r$ is called the planarity rank for variety $V$. If such a number $r$ doesn't exist, then we say that the variety $V$ has the infinite planarity rank. We prove that a non-trivial variety of commutative semigroups either has the infinite planarity rank and coincides with the variety of semigroups with the zero multiplication or has a planarity rank $1$, $2$ or $3$. These estimates of planarity ranks for varieties of commutative semigroups are achievable.
Keywords: semigroup, Cayley graph of semigroup, variety of semigroups, free semigroup of variety, planarity rank for semigroup variety, commutative semigroup, variety of commutative semigroups, planarity rank for variety of commutative semigroups.
Bibliographic databases:
Document Type: Article
UDC: 512.572
Language: Russian
Citation: D. V. Solomatin, “The ranks of planarity for varieties of commutative semigroups”, Prikl. Diskr. Mat., 2016, no. 4(34), 50–64
Citation in format AMSBIB
\Bibitem{Sol16}
\by D.~V.~Solomatin
\paper The ranks of planarity for~varieties~of~commutative~semigroups
\jour Prikl. Diskr. Mat.
\yr 2016
\issue 4(34)
\pages 50--64
\mathnet{http://mi.mathnet.ru/pdm567}
\crossref{https://doi.org/10.17223/20710410/34/4}
Linking options:
  • https://www.mathnet.ru/eng/pdm567
  • https://www.mathnet.ru/eng/pdm/y2016/i4/p50
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Прикладная дискретная математика
    Statistics & downloads:
    Abstract page:320
    Full-text PDF :271
    References:397
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024