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On quaternion algebras over some extensions of quadratic number fields. (English) Zbl 1471.11283

Summary: Let \(p\) and \(q\) be two positive primes, let \(\ell\) be an odd positive prime and let \(F\) be a quadratic number field. Let \(K\) be an extension of \(F\) of degree \(\ell\) such that \(K\) is a dihedral extension of \(\mathbb{Q}\), or else let \(K\) be an abelian \(\ell\)-extension of \(F\) unramified over \(F\) whenever \(\ell\) divides the class number of \(F\). In this paper, we provide a complete characterization of division quaternion algebras \(H_K (p, q)\) over \(K\).

MSC:

11R52 Quaternion and other division algebras: arithmetic, zeta functions
16K20 Finite-dimensional division rings
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References:

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