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On the relation between hyperrings and fuzzy rings

Jeffrey Giansiracusa Orcid Logo, Jaiung Jun, Oliver Lorscheid

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

Swansea University Author: Jeffrey Giansiracusa Orcid Logo

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DOI (Published version): 10.1007/s13366-017-0347-5

Abstract

We construct a full embedding of the category of hyperfields into Dress's category of fuzzy rings and explicitly characterize the essential image --- it fails to be essentially surjective in a very minor way. This embedding provides an identification of Baker's theory of matroids over hype...

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Published in: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
ISSN: 0138-4821 2191-0383
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa32007
Abstract: We construct a full embedding of the category of hyperfields into Dress's category of fuzzy rings and explicitly characterize the essential image --- it fails to be essentially surjective in a very minor way. This embedding provides an identification of Baker's theory of matroids over hyperfields with Dress's theory of matroids over fuzzy rings (provided one restricts to those fuzzy rings in the essential image). The embedding functor extends from hyperfields to hyperrings, and we study this extension in detail. We also analyze the relation between hyperfields and Baker's partial demifields.
Keywords: fuzzy rings, hyperrings, hyperfields, hyperstructures, matroids
College: Faculty of Science and Engineering

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