info:eu-repo/semantics/article
Resolution of Algebraic Systems of Equations in the Variety of Cyclic Post Algebras
Date
2011-07Registration in:
Díaz Varela, José Patricio; López Martinolich, Blanca Fernanda; Resolution of Algebraic Systems of Equations in the Variety of Cyclic Post Algebras; Springer; Studia Logica; 98; 1; 7-2011; 307-330
0039-3215
1572-8730
CONICET Digital
CONICET
Author
Díaz Varela, José Patricio
López Martinolich, Blanca Fernanda
Abstract
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.