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, L, on a given finite field F( p), and conversely. There exists an interpretation Φ of the variety $${\mathcal{V}(L_{p,k})}$$ generated by L into the variety $${\mathcal{V}(F(p^k))}$$ generated by F( p) and an interpretation Φ of $${\mathcal{V}(F(p^k))}$$ into $${\mathcal{V}(L_{p,k})}$$ such that ΦΦ( B) = B for every $${B \in \mathcal{V}(L_{p,k})}$$ and ΦΦ( R) = R for every $${R \in \mathcal{V}(F(p^k))}$$. 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, Gröbner bases and algorithms programmed in Maple. [ABSTRACT FROM AUTHOR]