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A note on D. Quillen’s paper: 'Projective modules over polynomial rings' (Invent. Math. 36 (1976), 167–171)
- Source :
- Proceedings of the American Mathematical Society. 64:231-232
- Publication Year :
- 1977
- Publisher :
- American Mathematical Society (AMS), 1977.
-
Abstract
- We give a simplified proof to the following theorem due to D. Quillen: if A is a commutative noetherian ring of global dimension ⩽ 1 \leqslant 1 , then finitely generated projective modules over A [ T 1 , … , T n ] A[{T_1}, \ldots ,{T_n}] are extended from A. We prove also that if A is a commutative noetherian ring of global dimension d, then finitely generated projective modules of rank > d > d over A [ T 1 , … , T n ] A[{T_1}, \ldots ,{T_n}] are extended from A.
Details
- ISSN :
- 10886826 and 00029939
- Volume :
- 64
- Database :
- OpenAIRE
- Journal :
- Proceedings of the American Mathematical Society
- Accession number :
- edsair.doi...........37b321d9d200eb47aa118b13d64278a3