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 ( 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

Arithmetic and Polynomials over Fuzzy Rings

Andreas Dress and Walter Wenzel


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.

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

Related publications

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