Displaying similar documents to “Congruences generated by filters”

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.

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...

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...

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 , → , 1 ) be a Hilbert algebra. The monoid of all unary operations on A generated by operations α p : x ↦ ( p → 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...

Further results on neutral consensus functions

G. D. Crown, M.-F. Janowitz, R. C. Powers (1995)

Mathématiques et Sciences Humaines

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We use a set theoretic approach to consensus by viewing an object as a set of smaller pieces called “bricks”. A consensus function is neutral if there exists a family D of sets such that a brick s is in the output of a profile if and only if the set of positions with objects that contain s belongs to D. We give sufficient set theoretic conditions for D to be a lattice filter and, in the case of a finite lattice, these conditions turn out to be necessary. Ourfinal result, which involves...