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MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
113/2007

Algebraic, Tropical, and Fuzzy Geometry

Andreas Dress and Walter Wenzel

Abstract

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".

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

Related publications

inJournal
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