Let p and q be two positive primes, let ℓ be an odd positive prime and let F be a quadratic number field. Let K be an extension of F of degree ℓ such that K is a dihedral extension of Q, or else let K be an abelian ℓ-extension of F unramified over F whenever ℓ divides the class number of F. In this paper, we provide a complete characterization of division quaternion algebras HK(p, q) over K.
On quaternion algebras over some extensions of quadratic number fields
Acciaro V.;
2021-01-01
Abstract
Let p and q be two positive primes, let ℓ be an odd positive prime and let F be a quadratic number field. Let K be an extension of F of degree ℓ such that K is a dihedral extension of Q, or else let K be an abelian ℓ-extension of F unramified over F whenever ℓ divides the class number of F. In this paper, we provide a complete characterization of division quaternion algebras HK(p, q) over K.File in questo prodotto:
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