Displaying similar documents to “Filters of lattices with respect to a congruence”

Coaxial filters of distributive lattices

M. Sambasiva Rao (2023)

Archivum Mathematicum

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Coaxial filters and strongly coaxial filters are introduced in distributive lattices and some characterization theorems of p m -lattices are given in terms of co-annihilators. Some properties of coaxial filters of distributive lattices are studied. The concept of normal prime filters is introduced and certain properties of coaxial filters are investigated. Some equivalent conditions are derived for the class of all strongly coaxial filters to become a sublattice of the filter lattice. ...

Free trees and the optimal bound in Wehrung's theorem

Pavel Růžička (2008)

Fundamenta Mathematicae

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We prove that there is a distributive (∨,0,1)-semilattice of size ℵ₂ such that there is no weakly distributive (∨,0)-homomorphism from C o n c A to with 1 in its range, for any algebra A with either a congruence-compatible structure of a (∨,1)-semi-lattice or a congruence-compatible structure of a lattice. In particular, is not isomorphic to the (∨,0)-semilattice of compact congruences of any lattice. This improves Wehrung’s solution of Dilworth’s Congruence Lattice Problem, by giving the best...

On the lattice of n-filters of an LM n-algebra

Dumitru Buşneag, Florentina Chirteş (2007)

Open Mathematics

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For an n-valued Łukasiewicz-Moisil algebra L (or LM n-algebra for short) we denote by F n(L) the lattice of all n-filters of L. The goal of this paper is to study the lattice F n(L) and to give new characterizations for the meet-irreducible and completely meet-irreducible elements on F n(L).

Congruence lattices of intransitive G-Sets and flat M-Sets

Steve Seif (2013)

Commentationes Mathematicae Universitatis Carolinae

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An M-Set is a unary algebra 〈 X , M 〉 whose set M of operations is a monoid of transformations of X ; 〈 X , M 〉 is a G-Set if M is a group. A lattice L is said to be represented by an M-Set 〈 X , M 〉 if the congruence lattice of 〈 X , M 〉 is isomorphic to L . Given an algebraic lattice L , an invariant Π ( L ) is introduced here. Π ( L ) provides substantial information about properties common to all representations of L by intransitive G-Sets. Π ( L ) is a sublattice of L (possibly isomorphic to the trivial lattice), a Π -product lattice....