Hyperfields for Tropical Geometry I. Hyperfields and dequantization
By O. Y. Viro. 2010
84 citations recorded by the source corpus.
New hyperfields, that is fields in which addition is multivalued, are introduced and studied. In a separate paper these hyperfields are shown to provide a base for the tropical geometry. The main hyperfields considered here are classical number sets, such as the set of complex numbers, the set of real numbers, and the set of real non-negative numbers, with the usual multiplications, but new, multivalued additions. The new hyperfields are related with the classical fields and each other by dequantisations. For example, the new complex tropical field is a dequantization of the field of complex numbers.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/975308806719f111695c294991263444f3f37076
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- Algebraic Geometry Over Hyperrings (2015, methodology): “This work has been motivated by Viro’s paper [41].”