Resumen de R_álgebras de dimensión 2 y métricas del plano real

Santiago Mazuelas Franco

• The relation between complex numbers and euclidean plane geometry is widely known. For instance, by means of the identification of the real plane with the field of complex numbers we can represent the inversive euclidean group in the plane by the moebius group.

  In this paper we define and present the main properties of the different types of two dimensional lR_algebras, as well as the complex numbers. We show that there are only three types of two dimensional lR_algebras with unity: complex (C), paracomplex (M) or dual numbers (|D); we study the basic properties of these rings and his qeometric role in terms of plane metrics, for example we define the cycles, for the different geometry types, by means of cross ratios.