On stably free modules over Laurent polynomial rings
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- by Abed Abedelfatah
- Proc. Amer. Math. Soc. 139 (2011), 4199-4206
- DOI: https://doi.org/10.1090/S0002-9939-2011-10901-8
- Published electronically: April 21, 2011
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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.References
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Bibliographic Information
- Abed Abedelfatah
- Affiliation: Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel
- Email: abedelfatah@gmail.com
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 4199-4206
- MSC (2010): Primary 13Axx; Secondary 13A50
- DOI: https://doi.org/10.1090/S0002-9939-2011-10901-8
- MathSciNet review: 2823065