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MiS Preprint
112/2007

Arithmetic and Polynomials over Fuzzy Rings

Andreas Dress and Walter Wenzel

Abstract

We study the arithmetic in fuzzy rings and related structures as well as polynomials over these coefficient domains. Fuzzy rings are an appropriate tool for a unified approach to representable, oriented, and valuated matroids. On the other hand, the relatively new field of "Tropical Geometry" as well as "Classical Algebraic Geometry" exhibit several analogies. The methods developed in the present paper will in future research also be fundamental for a unified treatment of these disciplines.

Received:
Dec 20, 2007
Published:
Dec 20, 2007
MSC Codes:
08A72, 08A05, 11C08, 13F20, 14A05
Keywords:
field, homomorphism, semiring, fuzzy ring, Grassmann-Plücker map, matroid with coefficients, Zariski Topology, Algebraic and Tropical Geometry

Related publications

inJournal
2015 Repository Open Access
Andreas W. M. Dress and Walter Wenzel

Arithmetic and polynomials over fuzzy rings

In: Communications in algebra, 43 (2015) 3, pp. 1207-1231