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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On stably free modules over Laurent polynomial rings


Author: Abed Abedelfatah
Journal: Proc. Amer. Math. Soc. 139 (2011), 4199-4206
MSC (2010): Primary 13Axx; Secondary 13A50
Published electronically: April 21, 2011
MathSciNet review: 2823065
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Abstract: We prove constructively that for any finite-dimensional commutative ring $ R$ and $ n\geq\dim (R)+2$, the group $ \mathrm{E}_{n}(R[X,X^{-1}])$ acts transitively on $ \mathrm{Um}_{n}(R[X,X^{-1}])$. In particular, we obtain that for any finite-dimensional ring $ R$, every finitely generated stably free module over $ R[X,X^{-1}]$ of rank $ >\dim R$ is free; i.e., $ R[X,X^{-1}]$ is $ (\dim R)$-Hermite.


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Additional Information

Abed Abedelfatah
Affiliation: Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel
Email: abedelfatah@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10901-8
PII: S 0002-9939(2011)10901-8
Keywords: Stably free modules, Hermite rings, unimodular rows, Laurent polynomial rings, constructive mathematics
Received by editor(s): May 29, 2010
Received by editor(s) in revised form: September 25, 2010, and October 19, 2010
Published electronically: April 21, 2011
Communicated by: Harm Derksen
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.