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 innvariables. In this article, we studythe kernel of higher R-derivation D of A. It is shown that if R isa HCF ring and tr. degR (AD)⩽1 then AD=R[f] for some f ∈ A.