Resolution of Algebraic Systems of Equations in the Variety of Cyclic Post Algebras

There is a constructive method to define a structure of simple k-cyclic Post algebra of order p, Lp,k, on a given finite field F(pk), and conversely. There exists an interpretation Φ1 of the variety V(Lp,k) generated by Lp,k into the variety V(F(pk)) generated by F(pk) and an interpretation Φ2 of V(F(pk)) into V(Lp,k) such that Φ2Φ1(B) = B for every B ∈ V(Lp,k) and Φ1Φ2(R) = R for every R ∈ V(F(pk)). In this paper we show how we can solve an algebraic system of equations over an arbitrary cyclic Post algebra of order p, p prime, using the above interpretation, Gröbner bases and algorithms programmed in Maple.Fil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: López Martinolich, Blanca Fernanda. Universidad Nacional del Comahue; Argentin