On completing unimodular polynomial vectors of length three

Rao, Ravi A. (1991) On completing unimodular polynomial vectors of length three Transactions of the American Mathematical Society, 325 (1). pp. 231-239. ISSN 0002-9947

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Official URL: https://www.jstor.org/stable/2001668?seq=1#fndtn-p...

Related URL: http://dx.doi.org/10.2307/2001668

Abstract

It is shown that if R is a local ring of dimension three, with 1/2 ϵ R, then a polynomial three vector (v0(X), v1(X), v2(X)) over R[X] can be completed to an invertible matrix if and only if it is unimodular. In particular, if 1/3! ϵ R, then every stably free projective R[X1,…, Xn]-module is free.

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