✦ LIBER ✦
A polynomial bound on the number of comaximal localizations needed in order to make free a projective module
✍ Scribed by Gema M. Diaz–Toca; Henri Lombardi
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 203 KB
- Volume
- 435
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
✦ Synopsis
Let A be a commutative ring and M be a projective module of rank k with n generators. Let h = nk. Standard computations show that M becomes free after localizations in n k comaximal elements (see Theorem 5). When the base ring A contains a field with at least hk + 1 non-zero distinct elements we construct a comaximal family G with at most (hk + 1)(nk + 1) elements such that for each g ∈ G, the module M g is free over A[1/g].