In this paper we introduce the Jacobsthal quaternions and the Jacobsthal–Lucas quaternions and give some of their properties. We derive the relations between Jacobsthal quaternions and Jacobsthal–Lucas quaternions and we give the matrix representation of these quaternions.

The hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper we consider special kinds of hybrid numbers, namely the Jacobsthal and the Jacobsthal-Lucas hybrid numbers and we give some their properties.

The hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper, we introduce and study the Fibonacci and Lucas hybrinomials, i.e. polynomials, which are a generalization of the Fibonacci hybrid numbers and the Lucas hybrid numbers, respectively.