A Theory of Congruences and Birkhoff’s Theorem for Matroids

Veldsman, Stefan

doi:10.26181/25864915.v1

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A Theory of Congruences and Birkhoff’s Theorem for Matroids

journal contribution

posted on 2024-05-21, 02:40 authored by Stefan VeldsmanStefan Veldsman

Abstract: A congruence is de?ned 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.

History

Publication Date

2021-11-18

Journal

Mathematica Pannonica

Volume

27_NS1

Issue

2

Pagination

15p. (p. 164-178)

Publisher

Akadémiai Kiadó

ISSN

0865-2090

Rights Statement

© 2021 The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution NonCommercial 4.0 International License (https://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted use, distribution, and reproduction in any medium for non-commercial purposes, provided the original author and source are credited, a link to the CC License is provided, and changes – if any – are indicated.