An algorithm for the Quillen-Suslin theorem for monoid rings Original Research Article

Let k be a field, and let M be a commutative, seminormal, finitely generated monoid, which is torsionfree, cancellative, and has no nontrivial units. Gubeladze [8] proved that finitely generated projective modules over kM are free. This paper contains an algorithm for finding a free basis for a finitely generated projective module over kM. As applications one obtains new algorithms for the Quillen-Suslin Theorem for polynomial rings and Laurent polynomial rings, based on Quillenʹs proof.