A Note on Elementary Derivations
2000 Mathematics Subject Classification: Primary: 14R10. Secondary: 14R20, 13N15. 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 [5] 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...