  Two are the objectives of the present paper. First we study properties of a
differentially simple commutative ring R with respect to a set D of derivations
of R. Among the others we investigate the relation between the D-simplicity of
R and that of the local ring RP with respect to a prime ideal P of R and we
prove a criterion about the D- simplicity of R in case where R is a
1-dimensional (Krull dimension) finitely generated algebra over a field of
characteristic zero and D is a singleton set. The above criterion was quoted
without proof in an earlier paper of the author. Second we construct a special
class of iterated skew polynomial rings defined with respect to finite sets of
derivations of a ring R (not necessarily commutative) commuting to each other.
The important thing in this class is that, if R is a commutative ring, then its
differential simplicity is the necessary and sufficient condition for the
simplicity of the corresponding skew polynomial ring.
  Key-Words- Derivations, Differentially simple rings, Finitely-generated
algebras, Iterated skew polynomial rings, Simple rings.
