ADDITIVE SUBGROUPS GENERATED BY POLYNOMIAL VALUES ON RIGHT IDEALS

Let R be a prime ring with extended centroid C, ρ a nonzero right ideal of R and f(X ₁,…,X_t ) a nonzero polynomial over C. We determine the additive subgroup of RC generated by all elements f(x ₁,…,x_t ) for x ₁,…,x_t ∈ ρ C and obtain a result concerning an independence property of polynomials in prime rings.