Displaying similar documents to “A note on homomorphisms of Hilbert algebras.”

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.

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...

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.

Equational spectrum of Hilbert varieties

R. Padmanabhan, Sergiu Rudeanu (2009)

Open Mathematics

Similarity:

We prove that an equational class of Hilbert algebras cannot be defined by a single equation. In particular Hilbert algebras and implication algebras are not one-based. Also, we use a seminal theorem of Alfred Tarski in equational logic to characterize the set of cardinalities of all finite irredundant bases of the varieties of Hilbert algebras, implication algebras and commutative BCK algebras: all these varieties can be defined by independent bases of n elements, for each n > 1. ...

On ideals in Hilbert algebras

Wiesław Aleksander Dudek (1999)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

Annihilators and deductive systems in commutative Hilbert algebras

Ivan Chajda, Radomír Halaš, Young Bae Jun (2002)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The properties of deductive systems in Hilbert algebras are treated. If a Hilbert algebra H considered as an ordered set is an upper semilattice then prime deductive systems coincide with meet-irreducible elements of the lattice Ded H of all deductive systems on H and every maximal deductive system is prime. Complements and relative complements of Ded H are characterized as the so called annihilators in H .