On the generalized hypercentralizer of a Lie ideal in a prime ring
Let \(R\) be an associative ring with center \(Z(R)\) and let \(U\) be a noncentral Lie ideal of \(R\). For any \(x,y\in R\) set \([x,y]_1=xy-yx\), for \(n>1\) set \([x,y]_n=[[x,y]_{n-1},y]_1\), and set \(H=\{r\in R\mid[r,u^n]_m=0\) for all \(u\in U\) with \(n=n(r,u)\geq 1\) and \(m=m(r,u)\geq 1\}\). The main result in the paper proves that when \(R\) is a prime ring containing no nonzero nil right ideal then either \(H=Z(R)\) or \(R\) embeds in \(M_2(F)\) for \(F\) a field.
scientific article; zbMATH DE number 1279139