International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 11, Pages 681-693
doi:10.1155/S016117120311112X
Generalized join-hemimorphisms on Boolean algebras
Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional del Centro, Provincia of Buenos Aires, Tandil 7000, Argentina
Received 14 November 2001
Copyright © 2003 Sergio 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 introduce the notions of generalized join-hemimorphism and
generalized Boolean relation as an extension of the notions of
join-hemimorphism and Boolean relation, respectively. We prove a
duality between these two notions. We will also define a
generalization of the notion of Boolean algebra with operators by
considering a finite family of Boolean algebras endowed with a
generalized join-hemimorphism. Finally, we define suitable
notions of subalgebra, congruences, Boolean equivalence, and open
filters.