J-ideals of matrices over PIDs

Given a square matrix B over a commutative ring R and an ideal J of R the J-ideal N_J(B) is the ideal consisting of the polynomials f in R[X] for which  f(B) in M_n(J)  holds. J-ideals arise naturally in the study of integer-valued polynomials on a single matrix. If the underlying ring is a principal ideal domain it suffices to determine a finite number of polynomials in order to describe all J-ideals of B. In this talk, we discuss an algorithm to explicitly compute these polynomials.

This is joint work with Clemens Heuberger.