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June 6, 20261 citations

Skew braces with no proper left ideals

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CTCindy (Sin Yi) Tsang

Key Points

  • This paper aims to classify finite left-simple skew braces and understand their properties.
  • Explored characteristics of left-simple skew braces.
  • Analyzed the correspondence with minimal Hopf--Galois structures.
  • Utilized results from previous studies on Galois extensions.
  • Finite left-simple skew braces correspond precisely to minimal Hopf--Galois structures.
  • Identified unique properties of such skew braces in relation to Galois extensions.

Abstract

A skew brace A = (A, , ) is said to be left-simple if A1 and it has no left ideal other than 1 and A. The purpose of this paper is to give a partial classification of the finite left-simple skew braces. A result of Stefanello and Trappeniers implies that finite left-simple skew braces correspond precisely to minimal Hopf--Galois structures on finite Galois extensions of fields.

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Cite This Study

Cindy (Sin Yi) Tsang (2026) studied this question.

synapsesocial.com/papers/6a23bc0571a5da9775e776aehttps://doi.org/10.46298/jonas.17536
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