Some theorems about projective modules over polynomial rings
β Scribed by S.M Bhatwadekar; A Roy
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 480 KB
- Volume
- 86
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract We give a constructive proof of the fact that finitely generated projective modules over a polynomial ring with coefficients in a PrΓΌfer domain **R** with Krull dimension β€ 1 are extended from **R**. In particular, we obtain constructively that finitely generated projective **R**[__X__~
For several classes of commutative rings R it is known that every finitely generated projective R-modules is isomorphic to a direct sum of a free w x R-module and an invertible ideal of R. For instance, Steinitz 27 essenw x tially proved this for Dedekind domains. Serre 25 proved the same result for