Iterated power intersections of ideals in rings of iterated differential polynomials. (Q2853957)

Consider a commutative Noetherian domain \(S\) over the field of rationals \(\mathbb Q\). Denote by \(R\) an \(n\)-iterated skew polynomial extension of \(S\) with derivations. Let \(I\) be a proper ideal of \(R\) and \(I(1)=\bigcap_{k\geqslant 1}I^k\). Put by induction \(I(m+1)=\bigcap_{k\geqslant 1}I^k(m)\).NEWLINENEWLINE The main result of the paper shows that \(I(n+1)=0\). -- In particular if \(R\) is the universal envelope of a finite dimensional Lie algebra of characteristic zero, then \(I(2)=0\).