On the kernels of higher R-derivations of R[x1, ... xn]

Abstract

Let R be an integral domain and A = R[x1, . . . , xn] be the polynomial ring in n variables. In this article, we study the kernel of higher R-derivation D of A. It is shown that if R is a HCF ring and tr. degR(Aᴰ) ≤ 1 then Aᴰ = R[f] for some f ∈ A.