Bicomplex numbers as a normal complexified f-algebra

The algebra B of bicomplex numbers is viewed as a complexification the Archimedean f-algebra hyperbolic D. This lattice-theoretic approach allows us to establish new properties so-called D-norms. In particular, we show that D-norms generate same topology in B. We develop D-trigonometric form number which leads geometric interpretation nth roots terms polyhedral tori. use concepts developed, particular Riesz subnorm D-norm, study uniform convergence zeta and gamma functions. main result this paper generalization case Riemann functional equation Euler's reflection formula.