Higher relative primitive ideals

The main object of this note is to introduce a higher order analog of the so-called primitive ideal of relative to introduced by Jiang-Pellikaan-Siersma, where are germs of analytic subspaces of . Our treatment of the problem is ideal-theoretic throughout, using the notion of iterated higher differential operators. Some examples from singularity theory are worked out. We establish the connection between higher primitive ideals and (relative) symbolic powers of an ideal and give an effective algorithm to compute both.