Displaying similar documents to “Annihilators and deductive systems in commutative Hilbert algebras”

Remarks on commutative Hilbert algebras

Radomír Halaš (2002)

Mathematica Bohemica

Similarity:

The paper shows that commutative Hilbert algebras introduced by Y. B. Jun are just J. C. Abbot’s implication algebras.

Representation and duality for Hilbert algebras

Sergio Celani, Leonardo Cabrer, Daniela Montangie (2009)

Open Mathematics

Similarity:

In this paper we introduce a special kind of ordered topological spaces, called Hilbert spaces. We prove that the category of Hilbert algebras with semi-homomorphisms is dually equivalent to the category of Hilbert spaces with certain relations. We restrict this result to give a duality for the category of Hilbert algebras with homomorphisms. We apply these results to prove that the lattice of the deductive systems of a Hilbert algebra and the lattice of open subsets of its dual Hilbert...

Some properties of epimorphisms of Hilbert algebras

Dumitru Buşneag, Mircea Ghiţă (2010)

Open Mathematics

Similarity:

This paper represents a start in the study of epimorphisms in some categories of Hilbert algebras. Even if we give a complete characterization for such epimorphisms only for implication algebras, the following results will make possible the construction of some examples of epimorphisms which are not surjective functions. Also, we will show that the study of epimorphisms of Hilbert algebras is equivalent with the study of epimorphisms of Hertz algebras.