International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 589830, 16 pages
doi:10.1155/2009/589830
Hilbert algebras of fractions
Christina-Theresia Dan
The Faculty of Mathematics and Computer Science, University of Craiova, Al.I.Cuza street nr.13, 200585 Craiova, Romania
Abstract
Let A be a bounded Hilbert algebra and S a ∨¯-closed subset of A. The Hilbert algebra of fractions AS is studied regarding maximal and irreducible deductive systems. As important results, we can mention a necessary and sufficient condition for a Hilbert algebra of fractions to be local and the characterization of this kind of algebras as inductive limits of some particular directed systems.