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)

 
 

 

Nonextended quadratic forms over polynomial rings over power series rings


Author: Raman Parimala
Journal: Proc. Amer. Math. Soc. 83 (1981), 453-454
MSC: Primary 15A63; Secondary 18F25
DOI: https://doi.org/10.1090/S0002-9939-1981-0627667-5
MathSciNet review: 627667
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: If $ R$ is a complete discrete valuation ring, then every quadratic space over $ R[T]$ is extended from $ R$. We here show by an example that a corresponding result for higher-dimensional complete regular local rings is not valid.


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

  • [1] M. A. Knus, M. Ojanguren and R. Sridharan, Quadratic forms and Azumaya algebras, J. Reine Angew. Math. 303/304 (1978), 231-248. MR 514682 (81h:15016)
  • [2] T. Y. Lam, Serre's conjecture, Lecture Notes in Math., vol. 635, Springer-Verlag, Berlin and New York, 1978. MR 0485842 (58:5644)
  • [3] Raman Parimala, Quadratic forms over polynomial rings over Dedekind domains, Amer. J. Math. 100 (1978), 913-928. MR 610478 (82g:10041)
  • [4] S. Parimala and R. Sridharan, Projective modules over polynomial rings over division rings, J. Math. Kyoto Univ. 15 (1975), 129-148. MR 0376760 (51:12935)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 15A63, 18F25

Retrieve articles in all journals with MSC: 15A63, 18F25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0627667-5
Keywords: Projective modules, quadratic spaces, extendibility
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society