Nilpotency in left semi-braces

被引：4
作者：
Catino, Francesco [1 ]
Cedo, Ferran [2 ]
Stefanelli, Paola [1 ]
机构：
[1] Univ Salento, Dipartimento Matemat & Fis Ennio Giorgi, Via Provinciale, I-73100 Arnesano, Lecce, Italy
[2] Univ Autonoma Barcelona, Dept Matematiques, E-08193 Barcelona, Spain
来源：
JOURNAL OF ALGEBRA | 2022年 / 604卷
关键词：
Quantum Yang-Baxter equation; Set-theoretical solution; Brace; Semi-brace; Skew brace; SET-THEORETICAL SOLUTIONS; SKEW LEFT BRACES; BAXTER; PRODUCT; RINGS;
D O I：
10.1016/j.jalgebra.2022.04.004
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce left and right series of left semi-braces. This allows to define left and right nilpotent left semi-braces. We study the structure of such semi-braces and generalize some results, known for skew left braces, to left semi-braces. We study the structure of left semi-braces B such that the set of additive idempotents E is an ideal of B. Finally we introduce the concept of a nilpotent left semi-brace and we show that the multiplicative group of such semi-braces is nilpotent. (c) 2022 Elsevier Inc. All rights reserved.
引用
收藏
页码：128 / 161
页数：34
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