NDLI: Algebraic, tropical, and fuzzy geometry

Content Provider	Springer Nature Link
Author	Dress, Andreas Wenzel, Walter
Copyright Year	2011
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”.
Starting Page	431
Ending Page	461
Page Count	31
File Format	PDF
ISSN	01384821
Journal	Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
Volume Number	52
Issue Number	2
e-ISSN	21910383
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-03-30
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Algebraic and Tropical Geometry Field Ring Semiring Fuzzy ring Linearly ordered abelian group Valuation Ideal Prime ideal Polynomial function Polynomial Zariski Topology Irreducible closed set Variety Varieties and morphisms Fuzzy algebraic structures Polynomials Valuations and their generalizations Polynomial rings and ideals; rings of integer-valued polynomials Convex and Discrete Geometry Algebraic Geometry Algebra Geometry
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Geometry and Topology

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Algebraic, tropical, and fuzzy geometry