Nondefinability of projectivity in lattice varieties
type: Item
instance of: scholarly article
title: Nondefinability of projectivity in lattice varieties
zbMATH Open document ID: 0535.06005
DOI: 10.1007/BF01194536
author: Kirby A. Baker
published in: Algebra Universalis
publication date: 1983-01-01T00:00:00Z
review text: By showing how projectivities and weak projectivities can be built into lattice identities the author created one of the most important tools in the equational theory of lattices. Though, as he shows in the note under review, neither concept is first order definable in any lattice variety other than distributive lattices. In contrast, for any finite lattice there is a bound on the length of weak projectivities needed for the description of principal congruences in the associated variety.
Mathematics Subject Classification ID: 06B20
zbMATH DE Number: 3849291
zbMATH Keywords: first order definable
zbMATH Keywords: lattice variety
zbMATH Keywords: length of weak projectivities
zbMATH Keywords: principal congruences
reviewed by: Christian Herrmann
MaRDI profile type: Publication
cites work: Primitive Satisfaction and Equational Problems for Lattices and Other Algebras
cites work: Finite equational bases for finite algebras in a congruence-distributive equational class
cites work: Q3968992
cites work: The structure of relatively complemented lattices
cites work: Q3956998
cites work: Uniform congruence schemes
cites work: Weak (projective) radius and finite equational bases for classes of lattices
cites work: Algebras Whose Congruence Lattices are Distributive.
cites work: Congruence varieties
cites work: Para primal varieties: A study of finite axiomatizability and definable principal congruences in locally finite varieties
cites work: Q5609363
cites work: Primitive subsets of lattices
cites work: On free modular lattices generated by finite chains
full work available at URL: https://doi.org/10.1007/bf01194536
OpenAlex ID: W2040283073
Recommended article: Nonmodular lattice varieties
Recommended article: Non-axiomatizability of the amalgamation class of modular lattice varieties
Recommended article: Q4816466
Recommended article: Unreasonable lattices of quasivarieties
Recommended article: Variety-independence in lattice theory
Recommended article: Intersection of noncharacterizable varieties of lattices
Recommended article: Q4227132
Recommended article: Generalizing a non-existence theorem in finite projective planes
Recommended article: Q3322159
Recommended article: Projectivity in (bounded) commutative integral residuated lattices
description: scientific article; zbMATH DE number 3849291