Aspects of distributivity
type: Item
instance of: scholarly article
title: Aspects of distributivity
zbMATH Open document ID: 0541.06005
DOI: 10.1007/BF01182245
published in: Algebra Universalis
publication date: 1984-01-01T00:00:00Z
review text: According to an important theorem of Crawley and Dilworth every element in an algebraic strongly atomic distributive lattice has a unique irredundant decomposition into irreducibles. The paper contains extensions of this to non-atomic lattices and applications to congruence distributive algebraic structures, in particular lattices.
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 06B10
Mathematics Subject Classification ID: 08B10
zbMATH DE Number: 3859189
zbMATH Keywords: strongly atomic distributive lattice
zbMATH Keywords: irredundant decomposition
zbMATH Keywords: irreducibles
zbMATH Keywords: congruence distributive
reviewed by: Christian Herrmann
MaRDI profile type: Publication
cites work: Q3956998
cites work: A characterization of semi-distributivity
cites work: Decomposition Theory for Lattices Without Chain Conditions
cites work: Distributivity in lattices
cites work: The structure of relatively complemented lattices
cites work: On the distributivity of a lattice of lattice-congruences
cites work: Q3243317
cites work: Algebras Whose Congruence Lattices are Distributive.
cites work: Sublattices of a Free Lattice
cites work: Lattice varieties covering the smallest non-modular variety
cites work: Equational Bases and Nonmodular Lattice Varieties
cites work: Finite Sublattices of a Free Lattice
cites work: Free lattices
full work available at URL: https://doi.org/10.1007/bf01182245
OpenAlex ID: W4230789569
author: Robert P. Dilworth
description: scientific article; zbMATH DE number 3859189