A note on homomorphisms of Hilbert algebras.
Celani, Sergio (2002)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Celani, Sergio (2002)
International Journal of Mathematics and Mathematical Sciences
Similarity:
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...
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. ...
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.
Higson, Nigel, Kasparov, Gennadi (1997)
Electronic Research Announcements of the American Mathematical Society [electronic only]
Similarity:
Jānis Cīrulis (2008)
Open Mathematics
Similarity:
We characterise those Hilbert algebras that are relatively pseudocomplemented posets.
Bučkovska, Aneta (2001)
Novi Sad Journal of Mathematics
Similarity:
Dan, Christina-Theresia (2009)
International Journal of Mathematics and Mathematical Sciences
Similarity: