The concept of number in its most general meaning uni¯es not only common numbers
that all of us know from school, but also such objects as the quaternion, the octave,
the matrices, etc. Without denying the importance of numbers of all types, let us well
emphasize the class chain that has the following shape: natural ! integer ! rational !
real ! complex. At the same time our aim is to found the possibility of extending the
given above classi¯cation to numbers of high dimensionality, including those that obey
commutative-associative multiplication.