Locally nilpotent derivations of rings with roots adjoined (Q357520)

In the article under review, the authors study locally nilpotent derivations on commutative domains over a field of characteristic zero obtained from a given domain \(R\) by adding an element \(z\) satisfying that \(z^n\in R\) for some \(n>1\). They set up a general framework to deal with such extensions, which cleans up and unify many disparate results in the literature. General criteria to decide when such domains are rigid, i.e. admit no non zero locally nilpotent derivation, or not are given.NEWLINENEWLINEThe article is illustrated by many examples and applications of the theory, for instance to the study of locally nilpotent derivations on the Russell cubic threefold and certain Pham-Brieskorn singular threefolds.