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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on D. Quillen’s paper: “Projective modules over polynomial rings” (Invent. Math. 36 (1976), 167–171)
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by Moshe Roitman PDF
Proc. Amer. Math. Soc. 64 (1977), 231-232 Request permission

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.
References
  • Daniel Quillen, Projective modules over polynomial rings, Invent. Math. 36 (1976), 167–171. MR 427303, DOI 10.1007/BF01390008
  • H. Bass, $K$-theory and stable algebra, Inst. Hautes Études Sci. Publ. Math. 22 (1964), 5–60. MR 174604, DOI 10.1007/BF02684689
  • Hyman Bass, Libération des modules projectifs sur certains anneaux de polynômes, Séminaire Bourbaki, 26e année (1973/1974), Exp. No. 448, Lecture Notes in Math., Vol. 431, Springer, Berlin, 1975, pp. 228–354 (French). MR 0472826
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • 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