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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On completing unimodular polynomial vectors of length three


Author: Ravi A. Rao
Journal: Trans. Amer. Math. Soc. 325 (1991), 231-239
MSC: Primary 13C10; Secondary 19A13
MathSciNet review: 991967
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Abstract: It is shown that if $ R$ is a local ring of dimension three, with $ \frac{1} {2} \in R$, then a polynomial three vector $ ({v_0}(X),{v_1}(X),{v_2}(X))$ over $ R[X]$ can be completed to an invertible matrix if and only if it is unimodular. In particular, if $ 1/3! \in R$, then every stably free projective $ R[{X_1}, \ldots ,{X_n}]$-module is free.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-0991967-0
PII: S 0002-9947(1991)0991967-0
Article copyright: © Copyright 1991 American Mathematical Society