International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 589830, 16 pages
doi:10.1155/2009/589830
Research Article

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

Received 5 July 2009; Accepted 19 October 2009

Academic Editor: Heinz Gumm

Copyright © 2009 Christina-Theresia Dan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.