J. Patricio Díaz Varela

Free‐decomposability in varieties of semi‐Heyting algebras

In this paper we prove that the free algebras in a subvariety of the variety of semi-Heyting algebras are directly decomposable if and only if satisfies the Stone identity.

Free Q -distributive lattices from meet semilattices

Abstract In this paper we provide an explicit construction of the free Q-distributive lattice generated by a finite partially ordered set. The starting point is the construction of the free meet semilattice over a poset given by Horn and Kimura (Algebra Universalis 1 (1971) 26–38).

Free Double Ockham Algebras

ABSTRACT The variety O2 of double Ockham algebras consists of the algebras (A ∨, ∧, f,g 0,1) of type (2,2,1,1,0,0) where (A; ∨, ∧,f, 0,1) and (A; ∨, ∧,g 0,1) are Ockham algebras. In [16], M. Sequeira introduced several subvarieties of O2. In this paper we give a construction of free double Ockham algebras on a partially ordered set. We also describe free objects for the subvarieties of O2 considered in [16].

Factor congruences in BCK -algebras

In this paper, we characterize factor congruences in the quasivariety of BCK-algebras. As an application we prove that the free algebra over an infinite set of generators is indecomposable in any subvariety of BCK-algebras. We also study the decomposability of free algebras in the variety of hoop residuation algebras

Decomposability of free Tarski algebras

{(\mathcal {HBCK})}

Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism

and its subvarieties. We prove that free algebras in a non k-potent subvariety of

Regular elements and Kolmogorov translation in residuated lattices

{\mathcal {HBCK}}