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This paper is a continuation of a previous work by the author and G. Puninskiwhere iterated intersections of powers of ideals were studied in rings ofiterated differential polynomials. We present a method which can be used toshow that for every proper ideal $I$ of a suitable ring of iterateddifferential polynomials almost all iterated intersections of powers of $I$have to be zero. The setback of the method is that it works only if thederivations used in the construction of the ring of iterated differentialpolynomials satisfy additional assumptions. On the other hand, it can beapplied in cases which were not covered by the aforementioned work, for examplefor a universal enveloping algebra of a completely solvable Lie algebra over afield of positive characteristic.

Iterated power intersections of ideals in rings of iterated differential polynomials II