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.
Cindy (Sin Yi) Tsang (Thu,) studied this question.