On completing unimodular polynomial vectors of length three
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- by Ravi A. Rao
- Trans. Amer. Math. Soc. 325 (1991), 231-239
- DOI: https://doi.org/10.1090/S0002-9947-1991-0991967-0
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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.References
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Bibliographic Information
- © Copyright 1991 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 325 (1991), 231-239
- MSC: Primary 13C10; Secondary 19A13
- DOI: https://doi.org/10.1090/S0002-9947-1991-0991967-0
- MathSciNet review: 991967