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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on D. Quillen's paper: ``Projective modules over polynomial rings'' (Invent. Math. 36 (1976), 167-171)


Author: Moshe Roitman
Journal: Proc. Amer. Math. Soc. 64 (1977), 231-232
MSC: Primary 13C10; Secondary 14F05
DOI: https://doi.org/10.1090/S0002-9939-1977-0444638-1
MathSciNet review: 0444638
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Abstract: We give a simplified proof to the following theorem due to D. Quillen: if A is a commutative noetherian ring of global dimension $ \leqslant 1$, then finitely generated projective modules over $ 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$ over $ A[{T_1}, \ldots ,{T_n}]$ are extended from A.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0444638-1
Article copyright: © Copyright 1977 American Mathematical Society