An Algorithm for the Quillen–Suslin Theorem for Quotients of Polynomial Rings by Monomial Ideals

This paper presents an algorithm for the Quillen–Suslin Theorem for quotients of polynomial rings by monomial ideals, that is, quotients of the form A = k [ x0, . . . ,xn ] / I, with I a monomial ideal and k a field. Vorst proved that finitely generated projective modules over such algebras are free. Given a finitely generated module P, described by generators and relations, the algorithm tests whether P is projective, in which case it computes a free basis forP .