Semi-braces and the Yang-Baxter equation

In this paper we obtain new solutions of the Yang-Baxter equation that are left non-degenerate through left semi-braces, a generalization of braces introduced by Rump. In order to provide new solutions we introduce the asymmetric product of left semi-braces, a generalization of the semidirect product of braces, that allows us to produce several examples of left semi-braces.