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A Theory of Congruences and Birkhoff’s Theorem for Matroids
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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.
Title: A Theory of Congruences and Birkhoff’s Theorem for Matroids
Description:
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.
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