INVESTIGADORES
CELANI Sergio Arturo
artículos
Título:
Hilbert algebras with supremum
Autor/es:
SERGIO ARTURO CELANI Y DANIELA MONTANGIE
Revista:
ALGEBRA UNIVERSALIS
Editorial:
BIRKHAUSER VERLAG AG
Referencias:
Año: 2012
ISSN:
0002-5240
Resumen:
In this paper we will study the class of Hilbert algebras with supremum, i.e., Hilbert algebras where the associated order is a join-semilattice. We will simplify the duality given in CelaniCabrerMontangie, and apply it to develop a duality for Hilbert algebras with supremum. We shall prove that the ordered set of all ideals of a Hilbert algebra with supremum has a lattice structure. We will also see that in this lattice it is possible to define an implication, but the resulting structure is neither a Heyting algebra nor an implicative semilattice. Finally, we will give a dual description of the lattice of ideals of a Hilbert algebra with supremum.
