Let A = k[x1,⋯,xg] be a
finitely generated integral domain over a field k of characteristic zero. Let A denote
the integral closure of A in its quotient field. A well known result due to
A. Seidenberg says that any first order k-derivation of A can be extended
to A. This result is known to be false for higher order derivations. In this
paper, the authors investigate what types of higher derivations on A can be
extended to A. The main results are for higher derivations which are cup
products. Set Derk1(A) =Derk1(A)0 and inductively define Derkn(A)0 as
follows:
The authors show that if φ ∈Derkn(A)0, then φ(A) ⊆A. Various examples are
given which indicate that the above mentioned result is about as good as
possible.
