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Papers by Hernando Gaitan

Mathematica Bohemica, Jan 2, 2017

Enseñanza, 2009

By considering Stone algebras as Ockham algebras we prove that a Stone algebra is completely dete... more By considering Stone algebras as Ockham algebras we prove that a Stone algebra is completely determined by its endomorphism monoid.

We modify slightly the definition of H-partial functions given by Celani and Montangie (2012); th... more We modify slightly the definition of H-partial functions given by Celani and Montangie (2012); these partial functions are the morphisms in the category of H-space and this category is the dual category of the category with objects the Hilbert algebras with supremum and morphisms, the algebraic homomorphisms. As an application we show that finite pure Hilbert algebras with supremum are determined by the monoid of their endomorphisms.

Czechoslovak Mathematical Journal, 1996

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

for the financial support, which took the form of teaching assistantship during the regular terms... more for the financial support, which took the form of teaching assistantship during the regular terms and of research assistantship during the summers, of the last four and a half years. I also wish to show here my gratitude to the " Universidad de los Andes" in Venezuela for helping me financially in my graduate studies. This work is affectionally dedicated to my son Daniel Guillermo and to my wife Magdalena. we found an example of a proper quasivariety of p-algebras which generates the whole variety. In constructing such a quasivariety, we took full advantage of the. results obtained by Adams in [1]. We will present this example in the last section of this chapter. Basic Concepts of Universal Algebra An n-ary operation / on a set A is any function / : A**-* A. An algebra is an ordered pair (A] F) where A is a set and F is a set of operations on A. To each f € F corresponds a non-negative integer, namely: its arity. We will consider only algebras for which F is finite. The elements of F are called the basic operations of the algebra and the set A, its universe or carrier set. If F = {/j,..., /j^}, we often write {A] fi,ffg). If ni,... are the corresponding arities of the elements in F we say that A is an algebra of type (n^,...usually adopting the convention > • ' • > nj^. ]i {A', F) and (i4'; F') are algebras of the same type, there is a bijective correspondence between F and F' such that if /' € F' corresponds to / € F, both / and /' have the same arity. Since we always consider only algebras of the same type, we will use the same symbol for a given basic operation in all the algebras under consideration. Also, we will write A instead of {A; F) when this causes no confusion. There are three fundamental methods of constructing new algebras: the for mation of subalgebras, homomorphic images and direct products. If A and B are algebras of the same type, A is a subalgebra of By in symbols, A < B, if A Ç B and every basic operation of A is the restriction of the corresponding basic operation of B. A homomorphism from A to B is a function a : A-> B such that for any

JP Journal of Algebra, Number Theory and Applications

Divulgaciones Matematicas

Demonstratio Mathematica, 2014

In this note we prove that if two implication algebras have isomorphic monoids of endomorphisms t... more In this note we prove that if two implication algebras have isomorphic monoids of endomorphisms then they are isomorphic.

By applying a technique of Adams and Dziobiak it is proved that the lattice of quasivarieties of ... more By applying a technique of Adams and Dziobiak it is proved that the lattice of quasivarieties of the symmetric distributive lattices has the cardinality of the continuum.

In this note we prove that there is a least strict quasi variety (i.e., a quasi variety which is ... more In this note we prove that there is a least strict quasi variety (i.e., a quasi variety which is not a variety) of De Morgan algebras and that such a quasivariety is perhaps the only strict quasi variety enjoying the relative congruence extension property. §1. INTRODUCTION For a quasivar iety Q ami an algebra A E Q. let ConQ(A) = {0 E Con(A) : 04/0 E Q}. where Con(A) denotes the set of congruence relations on A. The elements of C:onQ(A) are called Q-congruences on A. A is said to have relative (to Q) congruence extension property (further on ReEP) if for every subalgebra B of A. any Q-congruence on B is the restriction of a Q-congruence on A. Q has ReEP if all of its elements have this property. The purpose of this note is to prove that there is a least strict quasivariety of De Morgan algebras and such a quasi variety is perhaps the only strict quasivariety enjoying ReEP. For more results in this direction we refer the reader to [3] and [7]. Recall that a De Morgan algebra is an algebra (A; 1\, V,' ,0,1) of type (~, 2, 1,0,0) such that the reduct (A; 1\, V, 0,1) is a bounded distributive lattice and the following identities are satisfied: X" = x (XVy)'=X'l\yl The lattice of subvarieties of De Morgan algebras is a four-element chain T C B c k c: M where T. B, K. and-,vf denote respectively the varieties of trivial. Boolean, Kleene and De Morgan algebras. There are three non-trivial subdirectly irreducible De Morgan algebras each of which generates one of the non-trivial varieties above: B is generated by the two-element chain 2 = {O, I}, K is generated by the three element chain 3 = {O, a, I} in which a' = a and M Research supported by the CDCHT (project C-507-91) of the University of the Andes,

Studia Logica - An International Journal for Symbolic Logic - SLOGICA, 2000

In this paper we describe the Priestley space of a quasi-Stone algebra and use it to show that th... more In this paper we describe the Priestley space of a quasi-Stone algebra and use it to show that the class of finite quasi-Stone algebras has the amalgamation property. We also describe the Priestley space of the free quasi-Stone algebra over a finite set.

Semigroup Forum, 2011

We prove that if two finite Tarski algebras have isomorphic endomorphism monoids then they are is... more We prove that if two finite Tarski algebras have isomorphic endomorphism monoids then they are isomorphic.