A note on semiprime skew left braces and related semidirect products
Abstract
In this paper, we focus on semiprime skew left braces provided by semidirect products. We show that if a semidirect product B1 B2 is semiprime and B1 is Artinian, then B1 must be semiprime. Moreover, we prove that the semidirect product of strongly semiprime skew left braces is strongly semiprime. Finally, following [Question 1]smoktunowicz2024more, we provide examples of skew left braces of abelian type that are non-simple and strongly prime.
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