On skew braces and their ideals

A. Konovalov; Agata Smoktunowicz; Leandro Vendramin

doi:10.1080/10586458.2018.1492476

On skew braces and their ideals

A. Konovalov
, Agata Smoktunowicz
, Leandro Vendramin

Research output: Contribution to journal › Article › peer-review

Abstract

We define combinatorial representations of finite skew braces and use this idea to produce a database of skew braces of small size. This database is then used to explore different concepts of the theory of skew braces such as ideals, series of ideals, prime and semiprime ideals, Baer and Wedderburn radicals and solvability. The paper contains several questions.

Original language	English
Pages (from-to)	95-104
Number of pages	10
Journal	Experimental Mathematics
Volume	30
Issue number	1
Early online date	22 Dec 2018
DOIs	https://doi.org/10.1080/10586458.2018.1492476
Publication status	Published - 2021

Keywords

Braces
Yang-Baxter equation
Radical rings

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10.1080/10586458.2018.1492476

Experimenting_with_braces
© 2018 Taylor & Francis Group, LLC. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at: https://doi.org/10.1080/10586458.2018.1492476
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Cite this

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title = "On skew braces and their ideals",

abstract = "We define combinatorial representations of finite skew braces and use this idea to produce a database of skew braces of small size. This database is then used to explore different concepts of the theory of skew braces such as ideals, series of ideals, prime and semiprime ideals, Baer and Wedderburn radicals and solvability. The paper contains several questions.",

keywords = "Braces, Yang-Baxter equation, Radical rings",

author = "A. Konovalov and Agata Smoktunowicz and Leandro Vendramin",

note = "The first-named author is partially supported by CCP CoDiMa (EP/M022641/1) and the OpenDreamKit Horizon 2020 European Research Infrastructures project (\#676541). The second-named author is supported by the ERC Advanced grant 320974. The third-named author is supported by PICT-201-0147, MATH-AmSud 17MATH-01 and ERC Advanced grant 320974.",

year = "2021",

doi = "10.1080/10586458.2018.1492476",

language = "English",

volume = "30",

pages = "95--104",

journal = "Experimental Mathematics",

issn = "1058-6458",

publisher = "Taylor and Francis",

number = "1",

}

TY - JOUR

T1 - On skew braces and their ideals

AU - Konovalov, A.

AU - Smoktunowicz, Agata

AU - Vendramin, Leandro

N1 - The first-named author is partially supported by CCP CoDiMa (EP/M022641/1) and the OpenDreamKit Horizon 2020 European Research Infrastructures project (#676541). The second-named author is supported by the ERC Advanced grant 320974. The third-named author is supported by PICT-201-0147, MATH-AmSud 17MATH-01 and ERC Advanced grant 320974.

PY - 2021

Y1 - 2021

N2 - We define combinatorial representations of finite skew braces and use this idea to produce a database of skew braces of small size. This database is then used to explore different concepts of the theory of skew braces such as ideals, series of ideals, prime and semiprime ideals, Baer and Wedderburn radicals and solvability. The paper contains several questions.

AB - We define combinatorial representations of finite skew braces and use this idea to produce a database of skew braces of small size. This database is then used to explore different concepts of the theory of skew braces such as ideals, series of ideals, prime and semiprime ideals, Baer and Wedderburn radicals and solvability. The paper contains several questions.

KW - Braces

KW - Yang-Baxter equation

KW - Radical rings

UR - https://arxiv.org/abs/1804.04106

U2 - 10.1080/10586458.2018.1492476

DO - 10.1080/10586458.2018.1492476

M3 - Article

SN - 1058-6458

VL - 30

SP - 95

EP - 104

JO - Experimental Mathematics

JF - Experimental Mathematics

IS - 1

ER -

On skew braces and their ideals

Abstract

Keywords

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H2020 OPENDREAMKIT: OPENDREAMKIT (partner)

CoDiMa: CoDiMa (CCP in the area of Computational Discrete Mathematics)

Olexandr Konovalov

YangBaxter - Combinatorial Solutions for the Yang-Baxter equation, Version 0.2.0 (GAP package)

YangBaxter - Combinatorial Solutions for the Yang-Baxter equation, Version 0.7.0 (GAP package)

gap-packages/YangBaxter: YangBaxter (all versions)

Erratum to the paper “On skew braces and their ideals”

Cite this

On skew braces and their ideals

Abstract

Keywords

Access to Document

Handle.net

Other files and links

Fingerprint

Projects

H2020 OPENDREAMKIT: OPENDREAMKIT (partner)

CoDiMa: CoDiMa (CCP in the area of Computational Discrete Mathematics)

Profiles

Olexandr Konovalov

Datasets

YangBaxter - Combinatorial Solutions for the Yang-Baxter equation, Version 0.2.0 (GAP package)

YangBaxter - Combinatorial Solutions for the Yang-Baxter equation, Version 0.7.0 (GAP package)

gap-packages/YangBaxter: YangBaxter (all versions)

Research output

Erratum to the paper “On skew braces and their ideals”

Cite this