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Nilpotency in left semi-braces
Preprint
10 October 2020
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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.