Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 30, No 4, (2004), 549p-570p
Let R be a UFD containing a field of characteristic 0, and
Bm = R[Y1, . . . , Ym] be a polynomial ring over R. It was conjectured in 
that if D is an R-elementary monomial derivation of B3 such that ker D is
a finitely generated R-algebra then the generators of ker D can be chosen to
be linear in the Yi ’s. In this paper, we prove that this does not hold for B4.
We also investigate R-elementary derivations D of Bm satisfying one or the
other of the following conditions:
(i) D is standard.
(ii) ker D is generated over R by linear constants.
(iii) D is fix-point-free.
(iv) ker D is finitely generated as an R-algebra.
(v) D is surjective.
(vi) The rank of D is strictely less than m.