IJPAM: Volume 23, No. 1 (2005)

RIGHT-SIDED IDEMPOTENT QUANTALES
AND ORTHOMODULAR LATTICES

Leopoldo Román$^1$, Rita Zuazua$^2$
$^1$Instituto de Matemáticas
Universidad Nacional Autonoma de Mexico - UNAM
Área de la Investigación Científica
Ciudad Universitaria, México D.F., 04510, MEXICO
e-mail: leopoldo@matem.unam.mx
$^2$ Instituto de Matemáticas
Universidad Nacional Autonoma de Mexico - UNAM
Unidad Morelia, MEXICO
e-mail: zuazua@matmor.unam.mx


To the Memory of Professor Víctor Neumann-Lara.


Abstract.Let $Q$ a Gelfand quantale. If $R(Q)$ denotes the subquantale of $Q$ of the right-sided elements, $R(Q)$ turns out to be an idempotent, right-sided quantale. The non-commutative binary operation $\&$ in this case is induced by a quantifier. Quantifiers for the lattice of the closed subspaces of a separable, infinite dimensional Hilbert space are trivial.

Received: May 16, 2005

AMS Subject Classification: 03G12, 06C15, 81P10

Key Words and Phrases: quantum logic, orthomodular lattice, quantale, residuated semigroup

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 23
Issue: 1