Hilbert algebras as implicative partial semilattices

Jānis Cīrulis

Displaying similar documents to “Hilbert algebras as implicative partial semilattices”

Adjoint Semilattice and Minimal Brouwerian Extensions of a Hilbert Algebra

Jānis Cīrulis (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Let $A : = (A, \to, 1)$ be a Hilbert algebra. The monoid of all unary operations on $A$ generated by operations $α_{p} : x \mapsto (p \to x)$ , which is actually an upper semilattice w.r.t. the pointwise ordering, is called the adjoint semilattice of $A$ . This semilattice is isomorphic to the semilattice of finitely generated filters of $A$ , it is subtractive (i.e., dually implicative), and its ideal lattice is isomorphic to the filter lattice of $A$ . Moreover, the order dual of the adjoint semilattice is a minimal Brouwerian extension of...

Representation of Hilbert algebras and implicative semilattices

Sergio Celani (2003)

Open Mathematics

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In this paper we shall give a topological representation for Hilbert algebras that extend the topological representation given by A. Diego in [4]. For implicative semilattices this representation gives a full duality. We shall also consider the representation for Boolean ring.

On JP-semilattices of Begum and Noor

Jānis Cīrulis (2013)

Mathematica Bohemica

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In recent papers, S. N. Begum and A. S. A. Noor have studied join partial semilattices (JP-semilattices) defined as meet semilattices with an additional partial operation (join) satisfying certain axioms. We show why their axiom system is too weak to be a satisfactory basis for the authors' constructions and proofs, and suggest an additional axiom for these algebras. We also briefly compare axioms of JP-semilattices with those of nearlattices, another kind of meet semilattices with a...

Some remarks on certain classes of semilattices.

Murty, P.V.Ramana, Murty, M.Krishna (1982)

International Journal of Mathematics and Mathematical Sciences

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Subdirectly irreducible sectionally pseudocomplemented semilattices

Radomír Halaš, Jan Kühr (2007)

Czechoslovak Mathematical Journal

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Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented...

Relative annihilator-preserving congruence relations and relative annihilator-preserving homomorphisms in bounded distributive semilattices

Sergio A. Celani (2015)

Open Mathematics

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In this paper we shall study a notion of relative annihilator-preserving congruence relation and relative annihilator-preserving homomorphism in the class of bounded distributive semilattices. We shall give a topological characterization of this class of semilattice homomorphisms. We shall prove that the semilattice congruences that are associated with filters are exactly the relative annihilator-preserving congruence relations.