An Associative Left Brace is a Ring
Rings and Algebras
2019-12-24 v3
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 Ced\'o, Gateva-Ivanova and Smoktunowicz.
Cite
@article{arxiv.1811.04894,
title = {An Associative Left Brace is a Ring},
author = {Ivan Lau},
journal= {arXiv preprint arXiv:1811.04894},
year = {2019}
}
Comments
Version 3: Introduction rewritten, reference added, referee comments incorporated. To appear in Journal of Algebra and Its Applications