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A note on representation of cyclotomic fields. (English) Zbl 0870.11068

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.

MSC:

11R18 Cyclotomic extensions
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References:

[1] Borevich Z. I., Shafarevich I. R.: Number Theory. Moscow (Russian, 3rd [New York ( · Zbl 0121.04202
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