An Associative Left Brace is a Ring

It is proved that if a left brace 𝐴 has the operation ∗ associative, then 𝐴 is a two-sided brace. Consequently, 𝐴 is a Jacobson radical ring. This answers a question of Cedó, Gateva-Ivanova and Smoktunowicz.

Journal of Algebra and Its Applications