Integral points of certain matrix schemes
type: Item
instance of: scholarly article
title: Integral points of certain matrix schemes
zbMATH Open document ID: 1278.13023
author: Jean Fresnel
published in: Archiv der Mathematik
publication date: 2013-07-19T00:00:00Z
review text: The paper is inspired by a question posed by \textit{D. Lorenzini} in [J. Algebra 371, 609--619 (2012; Zbl 1266.13014)]. ``Let \(R\) be an Eucledian domain, \(M_n(R)\) the \(R\)-module of matrices with \(n\) rows and \(n\) columns, \(V\) an intersection of \(n-1\) affine hyperplanes of \(M_n(R)\). Assume \(V\) is non empty. Then, for all \(a\) in \(R\), there exists a matrix in \(V\) with determinant equal to \(a\).''
reviewed by: Alessandra Bernardi
Mathematics Subject Classification ID: 13F10
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 6189586
zbMATH Keywords: Euclidean domain
zbMATH Keywords: scheme of matrices
zbMATH Keywords: hyperplane conditions
zbMATH Keywords: determinant
MaRDI profile type: Publication
full work available at URL: s00013-013-0521-4
OpenAlex ID: W2042791517
cites work: On the completion of a partial integral matrix to a unimodular matrix
cites work: On Spaces of Linear Transformations with Bounded Rank
cites work: About Euclidean rings
cites work: Elementary divisor domains and Bézout domains
cites work: ON THE MAXIMAL RANK IN A SUBSPACE OF MATRICES
cites work: Q3786559
cites work: Arithmetic over the rings of all algebraic integers.
DOI: 10.1007/S00013-013-0521-4
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description: scientific article; zbMATH DE number 6189586