000136427 001__ 136427 000136427 005__ 20240826132401.0 000136427 0247_ $$2doi$$a10.1016/j.aim.2024.109880 000136427 0248_ $$2sideral$$a139379 000136427 037__ $$aART-2024-139379 000136427 041__ $$aeng 000136427 100__ $$aBallester-Bolinches, A. 000136427 245__ $$aSoluble skew left braces and soluble solutions of the Yang-Baxter equation 000136427 260__ $$c2024 000136427 5060_ $$aAccess copy available to the general public$$fUnrestricted 000136427 5203_ $$aThe 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. 000136427 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000136427 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000136427 700__ $$aEsteban-Romero, R. 000136427 700__ $$0(orcid)0000-0003-4809-1784$$aJiménez-Seral, P.$$uUniversidad de Zaragoza 000136427 700__ $$aPérez-Calabuig, V. 000136427 7102_ $$12006$$2005$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Algebra 000136427 773__ $$g455 (2024), 109880 [27 pp.]$$pAdv. math.$$tAdvances in Mathematics$$x0001-8708 000136427 8564_ $$s530556$$uhttps://zaguan.unizar.es/record/136427/files/texto_completo.pdf$$yVersión publicada 000136427 8564_ $$s1299911$$uhttps://zaguan.unizar.es/record/136427/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000136427 909CO $$ooai:zaguan.unizar.es:136427$$particulos$$pdriver 000136427 951__ $$a2024-08-22-13:17:52 000136427 980__ $$aARTICLE