In this paper we study certain quaternion algebras and symbol algebras which split.

Abstract. In this paper we study special Fibonacci quaternions and special generalized Fibonacci-Lucas quaternions in quaternion algebras over finite fields.

In this paper, we introduce the generalized Fibonacci-Lucas quaternions and we prove that the set of these elements is an order-in the sense of ring theory-of a quaternion algebra. Moreover, we investigate some properties of these elements.

In this paper, we find a class of division quaternion algebras over the field Q (i) and a class of division symbol algebras over a cyclotomic field.

Let p and q be two positive prime integers. In this paper we obtain a complete characterization of division quaternion algebras HK(p, q) over the composite K of n quadratic number fields.