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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
first_indexed 2017-02-17T14:01:34Z
last_indexed 2020-07-15T18:48:46Z
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spelling 2020-07-15T15:17:10.8958821 v2 32007 2017-02-17 On the relation between hyperrings and fuzzy rings 03c4f93e1b94af60eb0c18c892b0c1d9 0000-0003-4252-0058 Jeffrey Giansiracusa Jeffrey Giansiracusa true false 2017-02-17 MACS 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. Journal Article Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 0138-4821 2191-0383 fuzzy rings, hyperrings, hyperfields, hyperstructures, matroids 31 12 2017 2017-12-31 10.1007/s13366-017-0347-5 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2020-07-15T15:17:10.8958821 2017-02-17T10:07:41.6023252 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Jeffrey Giansiracusa 0000-0003-4252-0058 1 Jaiung Jun 2 Oliver Lorscheid 3 0032007-17022017100829.pdf fuzzy-hyperring.pdf 2017-02-17T10:08:29.4800000 Output 322895 application/pdf Accepted Manuscript true 2018-06-26T00:00:00.0000000 true eng
title On the relation between hyperrings and fuzzy rings
spellingShingle On the relation between hyperrings and fuzzy rings
Jeffrey Giansiracusa
title_short On the relation between hyperrings and fuzzy rings
title_full On the relation between hyperrings and fuzzy rings
title_fullStr On the relation between hyperrings and fuzzy rings
title_full_unstemmed On the relation between hyperrings and fuzzy rings
title_sort On the relation between hyperrings and fuzzy rings
author_id_str_mv 03c4f93e1b94af60eb0c18c892b0c1d9
author_id_fullname_str_mv 03c4f93e1b94af60eb0c18c892b0c1d9_***_Jeffrey Giansiracusa
author Jeffrey Giansiracusa
author2 Jeffrey Giansiracusa
Jaiung Jun
Oliver Lorscheid
format Journal article
container_title Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
publishDate 2017
institution Swansea University
issn 0138-4821
2191-0383
doi_str_mv 10.1007/s13366-017-0347-5
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description 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.
published_date 2017-12-31T03:59:28Z
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score 11.090091

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