MiS Preprint Repository

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MiS Preprint

Algebraic, Tropical, and Fuzzy Geometry

Andreas Dress and Walter Wenzel


The relatively new field of "Tropical Geometry" and "Classical Algebraic Geometry" have much in common. In this paper, we present a unified approach to both of these fields by studying more general "Fuzzy Geometries" over fuzzy rings. It turns out that the fuzzy ring which underlies "Tropical Geometry" is the same as that belonging to "Valuated Matroids".

Dec 20, 2007
Dec 20, 2007
MSC Codes:
14A10, 08A72, 11C08, 13A18, 13F20
Algebraic and Tropical Geometry, semiring, fuzzyring, linearly ordered abelian group, prime ideal, polynomial function, Zariski Topology, irreducible closed set

Related publications

2011 Journal Open Access
Andreas W. M. Dress and Walter Wenzel

Algebraic, tropical, and fuzzy geometry

In: Beiträge zur Algebra und Geometrie, 52 (2011) 2, pp. 431-461