International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 11, Pages 681-693

Generalized join-hemimorphisms on Boolean algebras

Sergio Celani

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.


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.