Finite algebras with Abelian properties
type: Item
instance of: scholarly article
title: Finite algebras with Abelian properties
zbMATH Open document ID: 0654.08001
DOI: 10.1007/BF01229981
published in: Algebra Universalis
publication date: 1988-01-01T00:00:00Z
review text: The aim of the paper is to investigate finite strongly Abelian algebras -- algebras satisfying the strong term condition. It is proved that every locally finite strongly Abelian variety is residually small; however, there exists a finite strongly Abelian algebra generating a residually large variety. Locally finite strongly Abelian varieties with one operation are characterized and it is proved that these varieties are Hamiltonian; the differences between strongly Abelian algebras with one or more operations are explored. Every subalgebra distributive variety is strongly Abelian. A full characterization of locally finite subalgebra distributive varieties with one operation is given.
Mathematics Subject Classification ID: 08A05
Mathematics Subject Classification ID: 08B20
zbMATH DE Number: 4066982
zbMATH Keywords: strongly Abelian algebras
zbMATH Keywords: strong term condition
zbMATH Keywords: strongly Abelian variety
zbMATH Keywords: subalgebra distributive varieties
author: Jay Shapiro
reviewed by: Jaroslav Ježek
MaRDI profile type: Publication
cites work: Clones satisfying the term condition
cites work: Q3934450
cites work: A note on the congruence extension property
cites work: Varieties with modular subalgebra lattices
cites work: Congruence lattices of algebras of fixed similarity type. I
cites work: Q4195012
cites work: Q4771004
cites work: The structure of finite algebras
cites work: Finite equational bases for subalgebra distributive varieties
cites work: The fine spectrum of a variety
cites work: Some applications of the term condition
description: scientific article; zbMATH DE number 4066982