Kostra, J. A note on representation of cyclotomic fields. (English) Zbl 0870.11068 Acta Math. Inform. Univ. Ostrav. 4, No. 1, 29-35 (1996). The correspondence between a circulant matrix and its determinant is crucial. Let \(C_l\) be the set of all circulant matrices of degree \(l,l\) prime. A surjective homomorphism \(\phi : C_l \rightarrow \mathbb{Q}(\zeta_l)\) is defined, where \(\mathbb{Q}\) is the field of rational numbers and \(\zeta_l\) is \(l\)-th root of 1. Then a special subset \(C^*_l \subset C_l\) is considered, equipped later with special multiplication \(*\). An isomorphism: \((C^*_l, +,*)\sim \mathbb{Q}(\zeta_l)\) is proved. Reviewer: M.Paštéka (Ostrava) Cited in 2 Documents MSC: 11R18 Cyclotomic extensions Keywords:circulant matrix; root of unity; algebraic extension PDFBibTeX XMLCite \textit{J. Kostra}, Acta Math. Inform. Univ. Ostrav. 4, No. 1, 29--35 (1996; Zbl 0870.11068) Full Text: EuDML References: [1] Borevich Z. I., Shafarevich I. R.: Number Theory. Moscow (Russian, 3rd [New York ( · Zbl 0121.04202 [2] Davis P. J.: Circulant matrices. Wiley-Interscience publishers, John Wiley and sons, New York-Chichester-Brisbane-Toronto, 1979. · Zbl 0418.15017 [3] Newman M., Taussky O.: On a generalization of the normal basis in abelian algebraic number fields. Comm. Pure Appl. Math. 9 (1958), 85-91. · Zbl 0071.03308 · doi:10.1002/cpa.3160090106 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.