On locally finite varieties with undecidable equational theory.
type: Item
instance of: scholarly article
title: On locally finite varieties with undecidable equational theory.
zbMATH Open document ID: 1058.08003
author: Marcel Jackson
published in: Algebra Universalis
publication date: 2005-04-19T00:00:00Z
review text: A variety \(\mathcal V\) is pseudorecursive if every finitely generated \(\mathcal V\)-free algebra has a decidable word problem but the equational theory of \(\mathcal V\) is undecidable. It is known that undecidability of the equational theory implies the undecidability of the uniform word problem. It is easy to establish the existence of many pseudorecursive varieties, even varieties of groups. However, all explicitly described examples in the literature are either nonassociative groupoids or varieties of groupoids with additional operations. The author combines a known method with some existing results to construct comparatively basic pseudorecursive varieties of semigroups and of groups. A large class of examples is described.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08A50
Mathematics Subject Classification ID: 03B25
Mathematics Subject Classification ID: 03D35
Mathematics Subject Classification ID: 08B99
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 20M07
zbMATH DE Number: 2158760
zbMATH Keywords: pseudorecursive variety
zbMATH Keywords: word problem
zbMATH Keywords: membership problem
zbMATH Keywords: decidability
MaRDI profile type: Publication
full work available at URL: s00012-002-8169-0
OpenAlex ID: W2059569262
DOI: 10.1007/S00012-002-8169-0
description: scientific article; zbMATH DE number 2158760