Abstract
Let R be an Euclidean 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 not empty. Then, for all a in R, there exists a matrix in V with determinant equal to a.
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Fresnel, J. Points entiers de certains schémas de matrices. Arch. Math. 100, 521–531 (2013). https://doi.org/10.1007/s00013-013-0521-4
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DOI: https://doi.org/10.1007/s00013-013-0521-4