A new algorithm for the Quillen-Suslin theorem
type: Item
instance of: scholarly article
title: A new algorithm for the Quillen-Suslin theorem
zbMATH Open document ID: 0960.13010
author: Reinhard Laubenbacher
author: Cynthia J. Woodburn
published in: Beiträge zur Algebra und Geometrie
publication date: 2000-04-26T00:00:00Z
full work available at URL: https://eudml.org/doc/230465
full work available at URL: BAG
review text: Proceeding from their more general constructions [\textit{R. C. Laubenbacher} and \textit{C. J. Woodburn}, J. Pure Appl. Algebra 117-118, 395-429 (1997; Zbl 0887.13006)], the authors propose a new algorithm for a part of the inductive algorithm of \textit{A. Logar} and \textit{B. Sturmfels} [J. Algebra 145, No. 1, 231-239 (1992; Zbl 0747.13020)]. Namely, let \(K\) be a field, \(P\) be a finitely generated module over the ring of polynomials \(K[x_1,x_2, \dots, x_r,y]\), given as the kernel or the cokernel of a matrix with entries of this ring, \(M\) be a maximal ideal of \(K[x_1,x_2, \dots,x_r]\), \(P_M\) be the corresponding localized module over the ring \(K[x_1,x_2, \dots, x_r]_M[y]\). The algorithm decides, whether \(P_M\) is projective and computes a free basis for \(P_M\) in this case.
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 13C10
Mathematics Subject Classification ID: 19A49
zbMATH DE Number: 1428658
zbMATH Keywords: projective modules over polynomial rings
zbMATH Keywords: free basis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1428658