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.

Discussiones Mathematicae - General Algebra and Applications

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.

Quaternions are a four-dimensional hypercomplex number system discovered by Hamilton in 1843 and next intensively applied in mathematics, modern physics, computer graphics and other fields. After the discovery of quaternions, modified quaternions were also defined in such a way that commutative property in multiplication is possible. That number system called as commutative quaternions is intensively studied and used for example in signal processing. In this paper we define generalized commutative quaternions and next based on them we define and explore Fibonacci type generalized commutative quaternions.