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1. CMB 2009 (vol 53 pp. 77)
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Constructing (Almost) Rigid Rings and a UFD Having Infinitely Generated Derksen and Makar-Limanov Invariants An example is given of a UFD which has an infinitely generated Derksen invariant. The ring is "almost rigid" meaning that the Derksen invariant is equal to the Makar-Limanov invariant. Techniques to show that a ring is (almost) rigid are discussed, among which is a generalization of Mason's abc-theorem.
Categories:14R20, 13A50, 13N15 |
2. CMB 2009 (vol 52 pp. 535)
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A Note on Locally Nilpotent Derivations\\ and Variables of $k[X,Y,Z]$ We strengthen certain results
concerning actions of $(\Comp,+)$ on $\Comp^{3}$
and embeddings of $\Comp^{2}$ in $\Comp^{3}$,
and show that these results are in fact valid
over any field of characteristic zero.
Keywords:locally nilpotent derivations, group actions, polynomial automorphisms, variable, affine space Categories:14R10, 14R20, 14R25, 13N15 |