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On the relation between hyperrings and fuzzy rings
Jeffrey Giansiracusa,
Jaiung Jun,
Oliver Lorscheid
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
Swansea University Author: Jeffrey Giansiracusa
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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...
| Published in: | Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry |
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| ISSN: | 0138-4821 2191-0383 |
| Published: |
2017
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa32007 |
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| 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. |
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| Keywords: |
fuzzy rings, hyperrings, hyperfields, hyperstructures, matroids |
| College: |
Faculty of Science and Engineering |