On two-sided skew braces
Abstract
In order to study two-sided skew braces, we introduce the notion of weakly trivial skew braces. We give a classification of such skew braces and show that they are essential in the study of two-sided skew braces. As an application, we obtain new and generalize known results relating the additive and multiplicative group of two-sided skew braces. Further, we show that two a priori different notions of prime and semi-prime skew braces, as introduced by Konovalov, Smoktunowicz and Vendramin, coincide for two-sided skew braces.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2022
- DOI:
- 10.48550/arXiv.2208.04772
- arXiv:
- arXiv:2208.04772
- Bibcode:
- 2022arXiv220804772T
- Keywords:
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- Mathematics - Rings and Algebras;
- Mathematics - Group Theory;
- Mathematics - Quantum Algebra
- E-Print:
- 17 pages. Minor changes