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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
##### Keywords:
circulant matrix; root of unity; algebraic extension
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##### References:
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