Modular subalgebra lattices
type: Item
instance of: scholarly article
title: Modular subalgebra lattices
zbMATH Open document ID: 0708.08002
DOI: 10.1007/BF01182454
published in: Algebra Universalis
publication date: 1990-01-01T00:00:00Z
review text: The algebras \({\mathcal A}\) for which the subalgebra lattice Sub \({\mathcal A}\times {\mathcal A}\) is a modular lattice are studied. It is proved that if \({\mathcal A}\) is supposed to be, in addition, an idempotent algebra, then it is the trivial algebra with the exception of one two-element algebra. Another theorem states that if Sub \({\mathcal A}^ 4\) is modular, then \({\mathcal A}\) has to satisfy the term condition, i.e. it is Abelian. The paper contains also a characterization of varieties with distributive subalgebra lattices.
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 08B99
Mathematics Subject Classification ID: 06C05
Mathematics Subject Classification ID: 06D05
zbMATH DE Number: 4162961
zbMATH Keywords: hamiltonian variety
zbMATH Keywords: abelian algebras
zbMATH Keywords: distributive lattices
zbMATH Keywords: subalgebra lattice
zbMATH Keywords: modular lattice
zbMATH Keywords: idempotent algebra
author: Péter P. Pálfy
reviewed by: Ernest Płonka
MaRDI profile type: Publication
cites work: Varieties with modular subalgebra lattices
cites work: Q5840058
cites work: Algebras Whose Congruence Lattices are Distributive.
cites work: Modularity of the subgroup lattice of a direct square
cites work: Finite equational bases for subalgebra distributive varieties
cites work: Q3739181
cites work: Polynomial hyperforms
full work available at URL: https://doi.org/10.1007/bf01182454
OpenAlex ID: W2056146681
description: scientific article; zbMATH DE number 4162961