1 results
ON THE LND CONJECTURE
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 108 / Issue 3 / December 2023
- Published online by Cambridge University Press:
- 03 July 2023, pp. 412-421
- Print publication:
- December 2023
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- Article
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Let k be a field of characteristic zero and
$k^{[n]}$ the polynomial algebra in n variables over k. The LND conjecture concerning the images of locally nilpotent derivations arose from the Jacobian conjecture. We give a positive answer to the LND conjecture in several cases. More precisely, we prove that the images of rank-one locally nilpotent derivations of 
$k^{[n]}$ acting on principal ideals are MZ-subspaces for any 
$n\geq 2$, and that the images of a large class of locally nilpotent derivations of 
$k^{[3]}$ (including all rank-two and homogeneous rank-three locally nilpotent derivations) acting on principal ideals are MZ-subspaces.
