Nilpotency in left semi-braces

Abstract

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.

References in corpus (2)

• Radical and weight of skew braces and their applications to structure groups of solutions of the Yang-Baxter equation
• Set-theoretic solutions to the Yang-Baxter equation and generalized semi-braces

Cited by in corpus (4)

• Rota-Baxter operators on Clifford semigroups and the Yang-Baxter equation
• Set-theoretic solutions of the Yang-Baxter equation associated to weak braces
• Solutions of the Yang-Baxter equation and strong semilattices of skew braces
• Affine structures on groups and semi-braces