Publikace na Matematicko-fyzikální fakulta |
2013
Abstrakt
Let R be an n-iterated ring of differential polynomials over a commutative noetherian domain which is a Q-algebra. We will prove that for every proper ideal I of R, the (n + 1)-iterated intersection I(n + 1) of powers of I equals zero.
A standard application includes the freeness of non-finitely generated projective modules over such rings. If I is a proper ideal of the universal enveloping algebra of a finite-dimensional solvable Lie algebra over a field of characteristic zero, then we will improve the above estimate by showing that I(2) = 0.