INMABB 05456
INSTITUTO DE MATEMATICA BAHIA BLANCA
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
On Hilbert algebras with supremum generated by finite chains
Autor/es:
ALDO V. FIGALLO; ELDA PICK; SUSANA SAAD; MARTÍN FIGALLO
Lugar:
Bahía Blanca
Reunión:
Congreso; XII Congreso Dr. Antonio Monteiro; 2013
Institución organizadora:
UNS-INMABB
Resumen:
Hilbert algebras with supremum, i.e., Hilbert algebras where the associated order is a join--semilattice
were first considered by A.V. Figallo, G. Ram\'on and S. Saad in \cite{FRS}, and independently by S. Celani and D.
Montangie in \cite{CeMon}.
On the other hand, L. Monteiro introduced the notion of $n-$valued Hilbert algebras (see \cite{Mon}).
In this work, we investigate the class of $n-$valued Hilbert algebras with supremum, denoted $H^{\vee}_{n}$, i.e.,
$n-$valued Hilbert algebras where the associated order is a join--semilattice. The varieties $H^{\vee}_{n}$ are generated
by finite chains. The free $H^{\vee}_{n}-$algebra \, ${\bf Free}_{n+1}(r)$\,
with $r$ generators is studied. In particular, we determine an upper bound to the cardinal
of the finitely generated free algebra \, ${\bf Free}_{n+1}(r)$.
