On distributivity of the lattice of subquasivarieties of a locally finite semi-simple arithmetical variety
type: Item
instance of: scholarly article
title: On distributivity of the lattice of subquasivarieties of a locally finite semi-simple arithmetical variety
zbMATH Open document ID: 0548.08005
DOI: 10.1007/BF01191501
author: W. Dziobiak
published in: Algebra Universalis
publication date: 1984-01-01T00:00:00Z
review text: Theorem: The lattice of all subvarieties of a locally finite semi-simple arithmetical variety \({\mathbb{K}}\) is distributive iff \(s({\mathbb{K}})\) is a chain and an initial segment of \(S({\mathbb{K}})\), where \(S({\mathbb{K}})\) denotes the set of isomorphism types of finite simple algebras from \({\mathbb{K}}\) and \(s({\mathbb{K}})\) denotes the set of types of algebras from \(S({\mathbb{K}})\), which contain no trivial algebra.
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 08C15
zbMATH DE Number: 3873402
zbMATH Keywords: locally finite semi-simple arithmetical variety
zbMATH Keywords: isomorphism types
zbMATH Keywords: finite simple algebras
reviewed by: Ernest Płonka
MaRDI profile type: Publication
cites work: Congruence Relations in Direct Products
full work available at URL: https://doi.org/10.1007/bf01191501
OpenAlex ID: W349451237
description: scientific article; zbMATH DE number 3873402