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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A stably elementary homotopy
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by Ravi A. Rao
Proc. Amer. Math. Soc. 137 (2009), 3637-3645
DOI: https://doi.org/10.1090/S0002-9939-09-09949-3
Published electronically: June 16, 2009

Abstract:

If $R$ is an affine algebra of dimension $d$ over a perfect C$_1$ field and $\sigma \in SL_{d + 1}(R)$ is a stably elementary matrix, we show that there is a stably elementary matrix $\sigma (X) \in SL_{d + 1}(R[X])$ with $\sigma (1) = \sigma$ and $\sigma (0) = I_{d + 1}$.
References
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Bibliographic Information
  • Ravi A. Rao
  • Affiliation: Tata Institute of Fundamental Research, Dr. Homi Bhabha Road, Navy Nagar, Mumbai 400 005, India
  • Email: ravi@math.tifr.res.in
  • Received by editor(s): November 12, 2007
  • Received by editor(s) in revised form: December 5, 2007, and February 27, 2009
  • Published electronically: June 16, 2009
  • Communicated by: Martin Lorenz
  • © Copyright 2009 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 3637-3645
  • MSC (2000): Primary 13C10, 19D45, 19G12, 55Q55
  • DOI: https://doi.org/10.1090/S0002-9939-09-09949-3
  • MathSciNet review: 2529870