doi:10.1016/j.aim.2024.109880engBallester-Bolinches, A.Esteban-Romero, R.Jiménez-Seral, P.Pérez-Calabuig, V.Soluble skew left braces and soluble solutions of the Yang-Baxter equationART-2024-139379The study of non-degenerate set-theoretic solutions of the Yang-Baxter equation calls for a deep understanding of the algebraic structure of a skew left brace. In this paper, the skew brace theoretical property of solubility is introduced and studied. It leads naturally to the notion of solubility of solutions of the Yang-Baxter equation. It turns out that soluble non-degenerate set-theoretic solutions are characterised by soluble skew left braces. The rich ideal structure of soluble skew left braces is also shown. A worked example showing the relevance of the brace theoretical property of solubility is also presented.2024http://zaguan.unizar.es/record/13642710.1016/j.aim.2024.109880http://zaguan.unizar.es/record/136427oai:zaguan.unizar.es:136427Advances in Mathematics 455 (2024), 109880 [27 pp.]byhttps://creativecommons.org/licenses/by/4.0/deed.esinfo:eu-repo/semantics/openAccess