{
  "annotation_id": "a85f5ba5-8be0-4de7-8f55-7cdf2fdfeadd",
  "date_created": "2026-02-17T05:53:19.966000Z",
  "date_modified": "2026-02-17T05:53:19.966000Z",
  "file_hash": "c7fffc1272d3202b1a5a24130faf8311527abf193b7d66c2779a5b3b7823ffca",
  "private": false,
  "record": {
    "abstract": "The aim of this paper is to take the study of Dedekind braces, that is, left braces for which every subbrace is an ideal, started in a previous paper, further. Dedekind braces $A$ whose additive group is non-periodic are analysed. We prove sufficient conditions for $A$ to be abelian: it is enough that every element is $2$-nilpotent for the star operation; and, if $A$ is hypermultipermutational, it suffices that the additive group of the socle is torsion-free. Both conditions can be translated in terms of set-theoretical solutions of the Yang-Baxter equation. In addition, we prove a structural theorem for the case of $A$ to be a multipermutational brace of level $2$.",
    "arxiv_id": "2601.09580",
    "authors": [
      "A. Ballester-Bolinches",
      "R. Esteban-Romero",
      "L. A. Kurdachenko",
      "V. P\u00e9rez-Calabuig"
    ],
    "categories": [
      "math.GR",
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "On left braces in which every subbrace is an ideal II",
    "url": "https://arxiv.org/abs/2601.09580",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7c0f97d6-a8ba-41ad-ab3b-cc3164e35af7",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}