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

摘要

There is a constructive method to define a structure of simple k-cyclic Post algebra of order p, L_(p,k), on a given finite field F(p~k), and conversely. There exists an interpretation Φ_1 of the variety V(L_(p,k)) generated by L_(p,k) into the variety V(F(p~k)) generated by F(p~k) and an interpretation Φ_2 of V(F(p~k)) into V(L_(p,k)) such that Φ_2Φ_1(B) = B for every B ∈ V(L_(p,k)) and Φ_1Φ_2(R) = R for every R ∈ V(F(p~k)). 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, Gr?bner bases and algorithms programmed in Maple.