Interpretability into Lukasiewicz algebras
In this paper we give a characterization of all the interpretations of the varieties of bounded distributive lattices, De Morgan algebras and Lukasiewicz algebras of order m in the variety of Lukasiewicz algebras of order n. In the case of distributive lattices we give a structure theorem that is generalized to De Morgan algebras and to Lukasiewicz algebras of order m. In the last two cases we also give the number of such interpretations.
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 ε V(Lp,k) and Φ1Φ2(R) = R for every R ε V(F(pk)).
Representing varieties of algebras by algebras
In this paper we describe a way of representing varieties of algebras by algebras. That is, to each variety of algebras we assign an algebra of a certain type, such that two varieties are rationallv equivalent if and only if the assigned algebras are isomorphic.