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On Unimodular Rows over Polynomial Rings

On Unimodular Rows over Polynomial Rings Let A be a commutative ring and n ≤ 3 a positive integer. In this paper, we consider unimodular rows (f 1(x),..., f n (x)) over A[x]. We prove that, if the row of the leading coefficients of f i (x) is unimodular over A and a ɛ A, then there exists β ɛ E n (A[x]) such that (f 1(x),...,f n (x))β = (f 1 (a),...,f n (a)). Also, if A is a Noetherian ring with finite Krull dimension and the row of leading coefficients satisfies the same condition, then we give a bound for the length of β in terms of elementary transvections. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algebra Colloquium Springer Journals

On Unimodular Rows over Polynomial Rings

Sivatski, A.
Algebra Colloquium , Volume 7 (2) – Jan 1, 2000
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Hong Kong
Subject
Mathematics; Algebra; Algebraic Geometry
ISSN
1005-3867
eISSN
0219-1733
DOI
10.1007/s10011-000-0197-8
Publisher site
See Article on Publisher Site

Abstract

Let A be a commutative ring and n ≤ 3 a positive integer. In this paper, we consider unimodular rows (f 1(x),..., f n (x)) over A[x]. We prove that, if the row of the leading coefficients of f i (x) is unimodular over A and a ɛ A, then there exists β ɛ E n (A[x]) such that (f 1(x),...,f n (x))β = (f 1 (a),...,f n (a)). Also, if A is a Noetherian ring with finite Krull dimension and the row of leading coefficients satisfies the same condition, then we give a bound for the length of β in terms of elementary transvections.

Journal

Algebra Colloquium – Springer Journals

Published: Jan 1, 2000

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