Geodesic
Matroids over a ring
Journal of the European Mathematical Society, Tome 18 (2016) no. 4, pp. 681-731.

Voir la notice de l'article provenant de la source EMS Press

We introduce the notion of a matroid M over a commutative ring R, assigning to every subset of the ground set an R-module according to some axioms. When R is a field, we recover matroids. When R=Z, and when R is a DVR, we get (structures which contain all the data of) quasi-arithmetic matroids, and valuated matroids, i.e. tropical linear spaces, respectively.
DOI : 10.4171/jems/600
Classification : 05-XX, 13-XX
Keywords: Matroid, module over Dedekind ring, arithmetic matroid, valuated matroid, arithmetic Tutte polynomial, tropical flag Dressian, Tutte–Grothendieck ring 
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Alex Fink; Luca Moci. Matroids over a ring. Journal of the European Mathematical Society, Tome 18 (2016) no. 4, pp. 681-731. doi : 10.4171/jems/600. http://geodesic.mathdoc.fr/articles/10.4171/jems/600/

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