A construction of loops which admit right alternative loop rings
It is known [see \textit{O. Chein} and \textit{E. G. Goodaire}, Algebras Groups Geom. 5, No. 3, 297-304 (1989; Zbl 0696.17016)] that -- if a loop ring \(RL\) is right alternative and \(\text{char }R\neq 2\), then \(RL\) is necessarily left alternative, -- if \(L\) is Moufang and if \(RL\) is right alternative (regardless of the characteristic of \(R\)), then \(RL\) must be left alternative. Thus if \(RL\) is a right, but not left, alternative ring, then \(\text{char }R\) must be 2 and \(L\) cannot be Moufang. Theorem 3.1. of this paper gives a specific construction of loops whose loop rings are right, but not left, alternative.
scientific article; zbMATH DE number 872698