Boolean products of indecomposables.
type: Item
instance of: scholarly article
title: Boolean products of indecomposables.
zbMATH Open document ID: 1060.08001
published in: Algebra Universalis
publication date: 2005-04-19T00:00:00Z
review text: It was proved recently by D. Vaggione that discriminator varieties \(V\) are characterized by two properties: (a) the Fraser-Horn property (FHP) and (b) \(V = I\Gamma ^{a}(V_{DI})\), where \(I\) denotes closure under isomorphism, \(\Gamma ^{a}\) denotes closure under formation of Boolean products with clopen equalizers, and \(V _{DI}\) is the class of directly indecomposable members of \(V\). He asked whether FHP could be replaced by the weaker property (BFC) of Boolean Factor Congruences. The author proves that if \(V\) satisfies (BFC) and \(V = I\Gamma ^{a}(V_{DI})\) then \(V_{DI}\) consists of simple algebras and it is a class defined by universal sentences.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08A05
Mathematics Subject Classification ID: 08B99
zbMATH DE Number: 2158824
zbMATH Keywords: Boolean factor congruences
zbMATH Keywords: Boolean product
zbMATH Keywords: directly indecomposable
zbMATH Keywords: discriminator variety
zbMATH Keywords: Fraser-Horn property
zbMATH Keywords: Pierce sheaf
author: Stanley N. Burris
MaRDI profile type: Publication
full work available at URL: s000120200015
OpenAlex ID: W2050794112
DOI: 10.1007/S000120200015
description: scientific article; zbMATH DE number 2158824