Mathematica Pannonica
Volume/Issue:
Volume 27_NS1: Issue 2

A Theory of Congruences and Birkhoff’s Theorem for Matroids

Author:
Stefan Veldsman Nelson Mandela University, Port Elizabeth, SOUTH AFRICA
La Trobe University, Melbourne, AUSTRALIA

Search for other papers by Stefan Veldsman in
Current site
Google Scholar
PubMed Close
Pages:
164–178
Online Publication Date:
28 Oct 2021
Publication Date:
18 Nov 2021
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2021.00015
Keywords:
matroid; matroid congruence; matroid isomorphism theorems; subdirect product of matroids; subdirectly irreducible matroid
Open access

A congruence is defined for a matroid. This leads to suitable versions of the algebraic isomorphism theorems for matroids. As an application of the congruence theory for matroids, a version of Birkhoff’s Theorem for matroids is given which shows that every nontrivial matroid is a subdirect product of subdirectly irreducible matroids.

  • [1]

    Arhangel’skiĭ, A. V. and Wiegandt, R. Connectednesses and disconectednesses in topology. General Topology and Appl. 5 (1975), 9–33.

    • Search Google Scholar
    • Export Citation
  • [2]

    Broere, I., Heidema J. and Veldsman, S. Congruences and Hoehnke radicals on graphs. Discuss. Math. Graph Theory 40 (4) (2020), 1067–1084.

    • Search Google Scholar
    • Export Citation
  • [3]

    Fried, E. and Wiegandt, R. Connectednesses and disconnectednesses of graphs. Algebra Univ. 5 (1975), 411–428.

  • [4]

    Gardner, B. J. and Wiegandt, R. The Radical Theory of Rings. Marcel Dekker Inc., 2004.

  • [5]

    Gordon, G. and McNulty, J. Matroids: a geometric introduction. University Press, Cambridge, 2012.

  • [6]

    Oxley, J. G. Matroid Theory. Oxford University Press, New York, 1992.

  • [7]

    Veldsman, S. Congruences on topological spaces with an application to radical theory. Alg. Universalis 80 (2019), article 25.

  • [8]

    Veldsman, S. Connectednesses of graphs and congruences. Asian-European Journal of Mathematics 14(10), (2021).

  • [9]

    Veldsman, S. Topological connectednesses and congruences. Quaestiones Mathematicae. (2020).

  • Collapse
  • Expand
Cover Mathematica Pannonica
Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752
The Instruction for Authors is available in PDF format. Please, download the file from HERE.
Please, download the LaTeX template from HERE.

Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
  • Sándor SZABÓ (University of Pécs)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz)
  • Ferenc HARTUNG (University of Pannonia, Veszprém)
  • Ferenc WEISZ (Eötvös University, Budapest)

Editorial Board

  • György DÓSA (University of Pannonia, Veszprém)
  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs)
  • Vedran KRCADINAC (University of Zagreb) 
  • Željka MILIN ŠIPUŠ (University of Zagreb)
  • Margit PAP (University of Pécs)
  • Mihály PITUK (University of Pannonia, Veszprém)
  • Jörg THUSWALDNER (Montanuniversität Leoben)
  • Zsolt TUZA (University of Pannonia, Veszprém)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics)  - Chair
  • Gabriella BÖHM (Akadémiai Kiadó, Budapest)
  • György GÁT (University of Debrecen)

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
(36) 72-503-600 / 4179
ltoth@gamma.ttk.pte.hu

  • Mathematical Reviews
  • Zentralblatt
  • DOAJ

Publication Model Gold Open Access
Submission Fee none
Article Processing Charge 0 EUR/article (temporarily)
Subscription Information Gold Open Access

Mathematica Pannonica
Language English
Size A4
Year of
Foundation		 1990
Volumes
per Year		 1
Issues
per Year		 2
Founder Akadémiai Kiadó
Founder's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Apr 2023 0 1 3
May 2023 0 2 1
Jun 2023 0 6 7
Jul 2023 0 2 6
Aug 2023 0 12 2
Sep 2023 0 5 3
Oct 2023 0 0 0