Derivations having divergence zero and closed polynomials over domains.

Let R be an integral domain. In this paper, we study the kernels of derivations of R [ 2 ] and closed polynomials in R [ n ] . Let D be an R -derivation of R [ 2 ] having divergence zero. In the first half of this paper, when R is a Q -domain, we give a necessary and sufficient condition for Ker D to be generated by one element over R . In the second half, we give some sufficient conditions for a non-constant polynomial to be closed in R [ n ] . [ABSTRACT FROM AUTHOR]