Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13C10, 14F05

Retrieve articles in all journals with MSC: 13C10, 14F05


Additional Information

Article copyright: © Copyright 1977 American Mathematical Society