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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:
20.12.07
Published:
20.12.07
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
