136427 20260217205526.0 doi 10.1016/j.aim.2024.109880 sideral 139379 ART-2024-139379 eng Ballester-Bolinches, A. Soluble skew left braces and soluble solutions of the Yang-Baxter equation 2024 Access copy available to the general public Unrestricted The 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. info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es 1.5 2024 MATHEMATICS 60 / 492 = 0.122 2024 Q1 T1 2.094 2024 Mathematics (miscellaneous) 2024 Q1 3.0 2024 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Esteban-Romero, R. Jiménez-Seral, P. Universidad de Zaragoza (orcid)0000-0003-4809-1784 Pérez-Calabuig, V. 2006 005 Universidad de Zaragoza Dpto. Matemáticas Área Algebra 455 (2024), 109880 [27 pp.] Adv. math. Advances in Mathematics 0001-8708 530556 http://zaguan.unizar.es/record/136427/files/texto_completo.pdf Versión publicada 1299911 http://zaguan.unizar.es/record/136427/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:136427 articulos driver 2026-02-17-20:30:51 ARTICLE