## On representation of cyclotomic fields $${\mathbb Q} (\zeta _{pq})$$.(English)Zbl 1024.11067

The correspondence between circulant matrices of degree $$pq$$ with $$p,q$$ primes and elements of cyclotomic fields $${\mathbb Q}(\zeta _{pq})$$ is found. This correspondence is via the determinant of a circulant matrix and the norm of an element of $${\mathbb Q}(\zeta _{pq})$$. This correspondence gives a representation for elements of given subfields of the cyclotomic field $${\mathbb Q}(\zeta _{pq})$$ by matrices.

### MSC:

 11R18 Cyclotomic extensions
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### References:

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