Alternative nucleus of right alternative algebras
Let R be a prime finitely generated right alternative algebra of characteristic \(\neq 2\) and let \(N_{\beta}=\{v\in R:\) \((a,a,v)=0\forall a\in R\}\) be the alternative nucleus of R. It is shown that if \([N_{\beta},R]\subseteq N_{\beta}\), then \(N_{\beta}\) coincides with the center of R, and if \([R,R]\subseteq N_{\beta}\) then R is alternative.
scientific article; zbMATH DE number 3995936