On the relation between hyperrings and fuzzy rings
Combinatorics
2016-08-03 v2 Commutative Algebra
Rings and Algebras
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.
Cite
@article{arxiv.1607.01973,
title = {On the relation between hyperrings and fuzzy rings},
author = {Jeffrey Giansiracusa and Jaiung Jun and Oliver Lorscheid},
journal= {arXiv preprint arXiv:1607.01973},
year = {2016}
}
Comments
22 pages, v2: strengthened result and added coauthor