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Experimental Mathematics Volume 30, 2021 - Issue 1
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Original Articles

On skew braces and their ideals

Alexander KonovalovCentre for Interdisciplinary Research in Computational Algebra, University of St Andrews, St Andrews, UK; ORCID Iconhttp://orcid.org/0000-0001-5299-3292View further author information
ORCID Icon,
Agata SmoktunowiczSchool of Mathematics, The University of Edinburgh, Edinburgh, UK; View further author information
&
Leandro VendraminIMAS–CONICET and Departamento de Matemática, FCEN, Universidad de Buenos Aires, Buenos Aires, ArgentinaCorrespondence[email protected]
ORCID Iconhttp://orcid.org/0000-0003-0954-7785View further author information
ORCID Icon
Pages 95-104 | Published online: 22 Dec 2018
 
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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 article contains several questions.

Acknowledgements

We thank Emiliano Acri, Ferran Cedó, Rofoldo Cossalter, Louis Rowen and Ivan Shestakov for comments and corrections.

Additional information

Funding

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 supprted by the European Research Council advanced grant [320974]. The thirdnamed author is supported by PICT-201-0147, MATH-AmSud 17MATH-01 and European Research Council advanced grant [320974].

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