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.

Nilpotency in left semi-braces

Catino, F.;Stefanelli, P.
2022-01-01

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/476872
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