✦ LIBER ✦
An Algorithm for the Quillen–Suslin Theorem for Quotients of Polynomial Rings by Monomial Ideals
✍ Scribed by Reinhard Laubenbacher; Karen Schlauch
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 307 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0747-7171
No coin nor oath required. For personal study only.
✦ Synopsis
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[x 0 , . . . , 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 for P .