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- Title
ON THE LND CONJECTURE.
- Authors
SUN, XIAOSONG; WANG, BEINI
- Abstract
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.
- Subjects
LOGICAL prediction; POLYNOMIAL rings; ALGEBRA; POLYNOMIALS
- Publication
Bulletin of the Australian Mathematical Society, 2023, Vol 108, Issue 3, p412
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S000497272300059X