A note on homomorphisms of Hilbert algebras
type: Item
instance of: scholarly article
title: A note on homomorphisms of Hilbert algebras
zbMATH Open document ID: 0993.03089
DOI: 10.1155/S0161171202011134
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/49359
full work available at URL: S0161171202011134.html
review text: Summary: 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 concept of homomorphism and with the deductive systems.
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 06F35
zbMATH DE Number: 1780317
zbMATH Keywords: representation theorem
zbMATH Keywords: Hilbert algebras
zbMATH Keywords: ordered sets
zbMATH Keywords: homomorphisms
zbMATH Keywords: irreducible deductive systems
zbMATH Keywords: order-ideal
author: Sergio A. Celani
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1780317