An equivalence between varieties of cyclic Post algebras and varieties generated by a finite field

In this paper we give a term equivalence between the simple k−cyclic Post algebra of order p, Lp,k, and the finite field F(pk) with constants F(p). By using Lagrange polynomials, we give an explicit procedure to obtain 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)). c Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved.