Hilbert algebras of fractions.

Dan, Christina-Theresia

Displaying similar documents to “Hilbert algebras of fractions.”

On ideals in Hilbert algebras

Wiesław Aleksander Dudek (1999)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Some properties of epimorphisms of Hilbert algebras

Dumitru Buşneag, Mircea Ghiţă (2010)

Open Mathematics

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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

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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...

Annihilators and deductive systems in commutative Hilbert algebras

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

Commentationes Mathematicae Universitatis Carolinae

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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 $H$ .