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)

 
 

 

On stably extended projective modules over polynomial rings


Author: Moshe Roitman
Journal: Proc. Amer. Math. Soc. 97 (1986), 585-589
MSC: Primary 13C10; Secondary 13F20, 18F25, 19A13
DOI: https://doi.org/10.1090/S0002-9939-1986-0845969-9
MathSciNet review: 845969
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove here that if $ A$ is a commutative noetherian ring of Krull dimension $ d$ and of finite characteristic prime to $ d!$, then stably extended projective $ A[{X_1}, \ldots ,{X_n}]$-modules of rank $ \geqslant d/2 + 1$ are extended from $ A$.


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

  • [1] H. Bass, Libération des modules projectifs sur certains anneaux de polynômes, Sém. Bourbaki 1973/74, exp. 448, Lecture Notes in Math., vol. 431, Springer-Verlag, Berlin and New York, 1975, pp. 228-254. MR 0472826 (57:12516)
  • [2] S. K. Gupta and M. P. Murthy, Suslin's work on linear groups over polynomial rings and Serre problem, 151 Lecture Notes, No. 8, The Macmillan Company of India Limited, Delhi.
  • [3] T. Y. Lam, Serre's conjecture, Lecture Notes in Math., vol. 635, Springer, 1978. MR 0485842 (58:5644)
  • [4] H. Lindel, Projective Moduln über Polynomring $ A[{T_1}, \ldots ,{T_m}]$ mit einem regulären Grundring A, Manuscripta Math. 23 (1978), 143-154. MR 0472912 (57:12597)
  • [5] -, On the Bass-Quillen conjecture concerning projective modules over polynomial rings, Invent. Math. 65 (1981), 319-323. MR 641133 (83g:13009)
  • [6] D. Quillen, Projective modules over polynomial rings, Invent. Math. 36 (1976), 167-171. MR 0427303 (55:337)
  • [7] R. A. Rao, On projective $ {R_{{f_1} \cdots {f_t}}}$-modules, Amer. J. Math. 107 (1985), 387-406. MR 784289 (86j:13011)
  • [8] M. Roitman, On unimodular rows, Proc. Amer. Math. Soc. 95 (1985), 184-188. MR 801320 (87f:13012)
  • [9] A. A. Suslin, On stably free modules, Mat. Sb. 102 (144) (1977), 537-550 (= Math. USSR-Sb. 31 (1977), 479-491). MR 0441949 (56:340)
  • [10] -, On the structure of the special linear group over polynomial rings, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), 235-252 (= Math. USSR Izv. 11 (1977), 221-238). MR 0472792 (57:12482)
  • [11] R. G. Swan, Projective modules over Laurent polynomial rings, Trans. Amer. Math. Soc. 237 (1978), 111-120. MR 0469906 (57:9686)
  • [12] L. N. Vaserstein, Operations on orbits of unimodular vectors, J. Algebra (to appear). MR 840588 (87j:13018)
  • [13] Ton Vorst, A survey on the $ K$-theory of polynomial extensions, Algebraic $ K$-Theory, Number Theory, Geometry and Analysis (Proc. Internat. Conf., Bielefeld, Germany, 1982), Lecture Notes in Math., vol. 1046, Springer, 1984, pp. 422-441. MR 750693 (86f:13008)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13C10, 13F20, 18F25, 19A13

Retrieve articles in all journals with MSC: 13C10, 13F20, 18F25, 19A13


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0845969-9
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society