Integral points of certain matrix schemes
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 \(a\).''
scientific article; zbMATH DE number 6189586
scientific article