Representation of Hilbert algebras and implicative semilattices

Sergio Celani

Displaying similar documents to “Representation of Hilbert algebras and implicative semilattices”

Hilbert algebras as implicative partial semilattices

Jānis Cīrulis (2007)

Open Mathematics

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The infimum of elements a and b of a Hilbert algebra are said to be the compatible meet of a and b, if the elements a and b are compatible in a certain strict sense. The subject of the paper will be Hilbert algebras equipped with the compatible meet operation, which normally is partial. A partial lower semilattice is shown to be a reduct of such an expanded Hilbert algebra i ?both algebras have the same ?lters.An expanded Hilbert algebra is actually an implicative partial semilattice...

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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Some remarks on distributive semilattices

Sergio A. Celani, Ismael Calomino (2013)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we shall give a survey of the most important characterizations of the notion of distributivity in semilattices with greatest element and we will present some new ones through annihilators and relative maximal filters. We shall also simplify the topological representation for distributive semilattices given in Celani S.A., Topological representation of distributive semilattices, Sci. Math. Japonicae online 8 (2003), 41–51, and show that the meet-relations are closed under...

Strong endomorphism kernel property for finite Brouwerian semilattices and relative Stone algebras

Jaroslav Guričan, Heghine Ghumashyan (2024)

Mathematica Bohemica

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We show that all finite Brouwerian semilattices have strong endomorphism kernel property (SEKP), give a new proof that all finite relative Stone algebras have SEKP and also fully characterize dual generalized Boolean algebras which possess SEKP.

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...

Flat semilattices

George Grätzer, Friedrich Wehrung (1999)

Colloquium Mathematicae

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