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 localisation principle for quadratic spaces over Laurent extensions


Authors: Raman Parimala and Parvin Sinclair
Journal: Proc. Amer. Math. Soc. 89 (1983), 202-204
MSC: Primary 11E88; Secondary 13C05
DOI: https://doi.org/10.1090/S0002-9939-1983-0712622-9
MathSciNet review: 712622
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove here that the localisation principle holds for anisotropic quadratic spaces over $ R[T,{T^{ - 1}}]$, where $ R$ is an integral domain in which 2 is invertible. We also give an example of an isotropic quadratic space over $ R[T,{T^{ - 1}}]$ for which the localisation principle does not hold.


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

  • [1] H. Bass, Algebraic $ K$-theory, Benjamin, New York, 1968. MR 0249491 (40:2736)
  • [2] M. A. Knus, R. Parimala and R. Sridharan, Non-free projective modules over $ {\mathbf{H}}[X,Y]$ and stable bundles over $ {{\mathbf{P}}_2}({\mathbf{C}})$, Invent. Math. 65 (1981), 13-27. MR 636877 (83d:13013)
  • [3] T. Y. Lam, Series summation of stably free modules, Quart. J. Math. Oxford Ser. (2) 27 (1976), 37-46. MR 0396678 (53:540)
  • [4] R. Parimala and R. Sridharan, A local global principle for quadratic forms over polynomial rings, J. Algebra 74 (1982), 264-269. MR 644232 (83h:10043)
  • [5] R. G. Swan, Projective modules over Laurent polynomial rings, Trans. Amer. Math. Soc. 237 (1978), 111-120. MR 0469906 (57:9686)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11E88, 13C05

Retrieve articles in all journals with MSC: 11E88, 13C05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0712622-9
Keywords: Laurent extensions, anisotropic, quadratic spaces, localisation principle
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society