On cyclic left modules and arbitrary bimodules over the octonions

Abstract

Qinghai Huo, Yong Li, Guangbin Ren described the structure of left $\mathbb{O}$-modules in great detail in arXiv:1911.08282. However, they left open a question on cyclic left $\mathbb{O}$-modules. This note intends to close this gap and provide a complete description of bimodules.