Quaternion algebras and symbol algebras over algebraic number field K, with the degree [K:Q] even

Abstract

Let F be a quadratic field (F = ℚ (√d), where d ≠ 0, 1 is a square-free integer). Let K be the pure algebraic quartic field K = ℚ (⁴√d). In this paper we determine connections between split quaternion algebras over F and split quaternion algebras over K.