An Associative Left Brace is a Ring
arXiv:1811.04894 · doi:10.1142/S0219498820501790
Abstract
It is proved that if a left brace has the operation associative, then is a two-sided brace. Consequently, is a Jacobson radical ring. This answers a question of Cedó, Gateva-Ivanova and Smoktunowicz.
Version 3: Introduction rewritten, reference added, referee comments incorporated. To appear in Journal of Algebra and Its Applications