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

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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), 933.

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  • [2]

    Broere, I., Heidema J. and Veldsman, S. Congruences and Hoehnke radicals on graphs. Discuss. Math. Graph Theory 40 (4) (2020), 10671084.

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  • [3]

    Fried, E. and Wiegandt, R. Connectednesses and disconnectednesses of graphs. Algebra Univ. 5 (1975), 411428.

  • [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).

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