Split epimorphisms and Baer sums of skew left braces

被引：0
|
作者：
Bourn, Dominique [1 ]
机构：
[1] Univ Littoral Cote dOpale, Lab Math Pures & Appl Joseph Liouville, UR 2597, LMPA, F-62100 Calais, France
来源：
JOURNAL OF ALGEBRA | 2024年 / 652卷
关键词：
Digroup; Skew brace; Yang-Baxter equation; Protomodular category; Strongly protomodular category; Split epimorphism; Baer sums;
D O I：
10.1016/j.jalgebra.2024.04.016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate the split epimorphisms in the categories of digroups and skew left braces. We show that, unlike the category DiGp of digroups, the category SkB of skew left braces is strongly protomodular. From that, we describe the expected Baer sums of exact sequences of skew left braces with abelian kernel. (c) 2024 Elsevier Inc. All rights reserved.
引用
收藏
页码：188 / 207
页数：20
相关论文
共 50 条
  • [31] Schreier split epimorphisms between monoids
    Dominique Bourn
    Nelson Martins-Ferreira
    Andrea Montoli
    Manuela Sobral
    Semigroup Forum, 2014, 88 : 739 - 752
  • [32] Schreier split epimorphisms between monoids
    Bourn, Dominique
    Martins-Ferreira, Nelson
    Montoli, Andrea
    Sobral, Manuela
    SEMIGROUP FORUM, 2014, 88 (03) : 739 - 752
  • [33] Solutions of the Yang-Baxter equation associated to skew left braces, with applications to racks
    Bachiller, David
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2018, 27 (08)
  • [34] Rota-Baxter groups, skew left braces, and the Yang-Baxter equation
    Bardakov, Valeriy G.
    Gubarev, Vsevolod
    JOURNAL OF ALGEBRA, 2022, 596 : 328 - 351
  • [35] ON SKEW QUASI-BAER RINGS
    Habibi, M.
    Moussavi, A.
    Manaviyat, R.
    COMMUNICATIONS IN ALGEBRA, 2010, 38 (10) : 3637 - 3648
  • [36] Skew left braces and isomorphism problems for Hopf-Galois structures on Galois extensions
    Koch, Alan
    Truman, Paul J.
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2023, 22 (05)
  • [37] Skew Polynomial Extensions of Semi Baer and Semi Quasi Baer Rings
    Patil, Avinash
    SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2020, 44 (01) : 99 - 104
  • [38] Skew left braces and 2-reductive solutions of the Yang-Baxter equation
    Jedlicka, Premysl
    Pilitowska, Agata
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2024, 228 (04)
  • [39] Skew Braces and the Braid Equation on Sets
    Rybolowicz, Bernard
    GEOMETRIC METHODS IN PHYSICS XL, WGMP 2022, 2024, : 145 - 152
  • [40] Symmetric skew braces and brace systems
    Bardakov, Valeriy G.
    Neshchadim, Mikhail V.
    Yadav, Manoj K.
    FORUM MATHEMATICUM, 2023, 35 (03) : 713 - 738
12345