The Quaternions can be generalized into further algebras called "quaternion algebras". This shows that the noncommutativity of quaternion multiplication comes from the multiplication of vector quaternions. The center of the quaternion algebra is the subfield of real quaternions. Examples include matrix algebras and quaternion algebras. Thus is isomorphic to the (generalized) quaternion algebra . Conjugation can be used to extract the scalar and vector parts of a quaternion. Its Lie algebra is the subspace of quaternion vectors. In computational implementations this requires two quaternion multiplications. This is a dual scalar which is the "magnitude squared" of the dual quaternion. The real component of a quaternion is also called its scalar part. Slerp also has expressions in terms of quaternion algebra, all using exponentiation. Three dimensional fractals are generated in a variety of ways including by using quaternion algebra. Sometimes a redundant fourth number is added to simplify operations with quaternion algebra. Note that the norm of a Hurwitz quaternion is always an integer. A quaternion that equals its vector part is called a "vector quaternion".