Idempotent Elements in Tricomplex Numbers

In 1892, in search for special algebras, Corrado Segre published a paper in which he introduced an infinite family of algebras whose elements are called bicomplex numbers, tricomplex numbers… , n – complex numbers. In that paper Segre introduced idempotent elements of bicomplex numbers. Idempotent elements play a central role in the theory of bicomplex numbers. This paper introduces the algebraic structure of Tricomplex Numbers exploring some of their fundamental properties. We have identified and characterized sixteen distinct idempotent elements of Tricomplex Numbers. We also discuss their properties and establish the relationships among them.