An Associative Left Brace is a Ring

Abstract

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.

Publication
Journal of Algebra and Its Applications
Ivan Lau
Ivan Lau
Research Assistant

I am interested in the theoretical and algorithmic aspects of machine learning and optimization.