On algebraic properties of bicomplex and hyperbolic numbers. (English) Zbl 1114.11033

The goal of this paper is to present some algebraic properties of both bicomplex numbers and hyperbolic numbers. In the first section there are introduced bicomplex numbers and a number of basic properties are indicated. Section 2 deals with some types of conjugations of bicomplex numbers, which extend the usual complex one. In Sections 3 and 4 there are studied the different types of moduli of the above numbers. Hyperbolic numbers and their properties are investigated in Section 5.
Here, for hyperbolic numbers there are also specified the properties already established for bicomplex numbers. In the last section all these algebraic structures are regarded in the specific context of Clifford algebras.
All results are new and carefully proved. The manner of presenting is clear and so the paper contributes to the development of this research domain.


11E88 Quadratic spaces; Clifford algebras
15A66 Clifford algebras, spinors
30G35 Functions of hypercomplex variables and generalized variables