标题： 斜括号中下和上中心序列的类比：综述 显示英文标题

标题： Analogs of the lower and upper central series in skew braces: a survey

摘要： 一个反括号是一个类似环和群的代数结构，它是在研究Yang-Baxter方程的集合论解时引入的。 在本文综述中，我们将考虑反括号的左系列、右系列、socle系列和消去子系列。 它们可以看作是群的下中心系列和上中心系列的类似物。 除了这些系列的一些已知事实外，我们将证明关于它们各项之间关系的几个新结果。 我们还将考虑由Bonatto和Jedlička定义的反括号的下中心系列。 正如我们将解释的那样，它似乎是对反括号的下中心系列的“正确”类比。 关于这一点，我们还将讨论Ballester-Bolinches等人提出的理想下中心系列的概念。 显示英文摘要

摘要： A skew brace is a ring-like and group-like algebraic structure that was introduced in the study of set-theoretic solutions to the Yang-Baxter equation. In this survey paper, we shall consider the left series, right series, socle series, and annihilator series of skew braces. They may be regarded as analogs of the lower and upper central series of groups. Other than some well-known facts regarding these series, we shall prove several new results about the relationship among their terms. We shall also consider the lower central series of skew braces that was defined by Bonatto and Jedli\v{c}ka. As we shall explain, it seems to be the ``correct" analog of the lower central series for skew braces. Concerning this, we shall also discuss the notion of the lower central series of ideals that is due to Ballester-Bolinches et al.