A note on quillen’s paper “projective modules over polynomial rings”

Moshe Roitman

doi:10.1090/S0002-9939-1977-0444638-1

A note on quillen’s paper “projective modules over polynomial rings”

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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 < 1, then finitely generated prqjective modules over A[TX,., Tn] 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[TX,., Tn] are extended from A.

Original language	English
Pages (from-to)	231-232
Number of pages	2
Journal	Proceedings of the American Mathematical Society
Volume	64
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1977-0444638-1
State	Published - Jun 1977
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-1977-0444638-1

Cite this

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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 < 1, then finitely generated prqjective modules over A[TX,., Tn] 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[TX,., Tn] are extended from A.",

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A note on quillen’s paper “projective modules over polynomial rings”

Abstract

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