On McKenzie's method
type: Item
instance of: scholarly article
title: On McKenzie's method
zbMATH Open document ID: 0856.08005
DOI: 10.1007/BF01879739
author: Ross Willard
published in: Periodica Mathematica Hungarica
publication date: 1996-09-15T00:00:00Z
review text: Let \(A\) be an algebra, for every cardinal \(\lambda\) let \(\lambda^+\) denote the successor cardinal to \(\lambda\) and let \(\kappa(A)\) denote the supremum over all cardinalities \(|S|^+\) where \(S\) runs through all non-trivial subdirectly irreducible algebras belonging to the variety generated by \(A\). An explicit description for a method discovered by McKenzie allowing to construct a finite algebra \(B\) of finite type with \(\kappa(B)= \omega_1\) is given.
reviewed by: Helmut Länger
Mathematics Subject Classification ID: 08B26
zbMATH DE Number: 926948
zbMATH Keywords: finitely generated variety
zbMATH Keywords: RS conjecture
zbMATH Keywords: subdirectly irreducible algebras
MaRDI profile type: Publication
cites work: On infinite subdirectly irreducible algebras in locally finite equational classes
cites work: The structure of finite algebras
cites work: THE RESIDUAL BOUNDS OF FINITE ALGEBRAS
cites work: THE RESIDUAL BOUND OF A FINITE ALGEBRA IS NOT COMPUTABLE
cites work: Q3658046
cites work: Equational classes generated by finite algebras
cites work: A RESIDUALLY SMALL, FINITELY GENERATED, SEMI-SIMPLE VARIETY WHICH IS NOT RESIDUALLY FINITE
full work available at URL: https://doi.org/10.1007/bf01879739
OpenAlex ID: W1979441702
description: scientific article; zbMATH DE number 926948