International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 1, Pages 55-61

A note on homomorphisms of Hilbert algebras

Sergio Celani

Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional del Centro, Pinto 399, Tandil 7000, Argentina

Received 21 November 2000; Revised 14 May 2001

Copyright © 2002 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 give a representation theorem for Hilbert algebras by means of ordered sets and characterize the homomorphisms of Hilbert algebras in terms of applications defined between the sets of all irreducible deductive systems of the associated algebras. For this purpose we introduce the notion of order-ideal in a Hilbert algebra and we prove a separation theorem. We also define the concept of semi-homomorphism as a generalization of the similar notion of Boolean algebras and we study its relation with the homomorphism and with the deductive systems.