International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 21835, 20 pages
doi:10.1155/IJMMS/2006/21835
Simple and subdirectly irreducibles bounded distributive lattices
with unary operators
Consejo Nacional de Investigaciones Científicas Y Técnicas (CONICET) and Departamento de Matemáticas, Facultad de Ciencias Exactas, Universidad Nacional del Centro de la Provincia de Buenos Aires, Pinto 399, Tandil 7000, Argentina
Received 27 February 2005; Revised 15 July 2006; Accepted 18 July 2006
Copyright © 2006 Sergio Arturo Celani. 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
We characterize the simple and subdirectly irreducible distributive algebras in
some varieties of distributive lattices with unary operators, including topological and monadic positive modal algebras. Finally, for some varieties of Heyting algebras with operators we apply these results to determine the simple and subdirectly irreducible algebras.