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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Stably free modules over $\mathbf {R}{[X]}$ of rank $> \dim \mathbf {R}$ are free
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by Ihsen Yengui PDF
Math. Comp. 80 (2011), 1093-1098 Request permission


We prove that for any finite-dimensional ring $\mathbf {R}$ and $n\geq \dim \mathbf {R} +2$, the group $\textrm {E}_{n}(\textbf {R}[X])$ acts transitively on $\textrm {Um}_{n}(\mathbf {R}[X])$. In particular, we obtain that for any finite-dimensional ring $\mathbf {R}$, all finitely generated stably free modules over $\mathbf {R}[X]$ of rank $> \dim \mathbf {R}$ are free. This result was only known for Noetherian rings. The proof we give is short, simple, and constructive.
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Additional Information
  • Ihsen Yengui
  • Affiliation: Department of Mathematics, Faculty of Sciences of Sfax, 3000 Sfax, Tunisia
  • MR Author ID: 657905
  • Email:
  • Received by editor(s): June 13, 2009
  • Published electronically: September 27, 2010
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 80 (2011), 1093-1098
  • MSC (2010): Primary 13C10, 19A13, 14Q20, 03F65
  • DOI:
  • MathSciNet review: 2772113