In this subsection, we will assume that R is a prime ring that H is a generalization of R, that L is a noncentral Lie
idyllic of R, and that 0≠ ࢻ ∋ ࡾ .If s, t ≥ 0 and n > 0, then for all u in L, aus(H(u)n)u(t) must equal 0. All of them fit neatly inside
the specified ranges of integers. H(x) = bx for every x ∈ R if and only if s = 0 and b = 0; this is not the case if R satisfy s4, the
normal uniqueness in four variables.