Derivations having divergence zero onR[X,Y] |
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| Authors: | Joost Berson Arno van den Essen Stefan Maubach |
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| Affiliation: | (1) Department of Mathematics, University of Nijmegen Toernooiveld, 6525 ED Nijmegen, The Netherlands |
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| Abstract: | In this paper it is proved that for any ℚ-algebraR any locally nilpotentR-derivationD onR[X,Y] having divergence zero and 1 ∈ (D(X),D(Y)) (i) has a slice, and (ii)A D =R[P] for someP. Furthermore, it is shown that any surjectiveR-derivation onR[X,Y] having divergence zero is locally nilpotent. Connections with the Jacobian Conjecture are made. |
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