  We consider Clifford algebras over the field of real or complex numbers as a
quotient algebra without fixed basis. We present classification of Clifford
algebra elements based on the notion of quaternion type. This classification
allows us to reveal and prove a number of new properties of Clifford algebras.
We rely on the operations of conjugation to introduce the notion of quaternion
type. Also we find relations between the concepts of quaternion type and rank
of Clifford algebra element.
