Lattices of equational theories are congruence lattices of monoids with one additional unary operation
type: Item
instance of: scholarly article
title: Lattices of equational theories are congruence lattices of monoids with one additional unary operation
zbMATH Open document ID: 0789.08006
DOI: 10.1007/BF01196092
author: Norbert Newrly
published in: Algebra Universalis
publication date: 1994-06-14T00:00:00Z
review text: In Stud. Sci Math. Hung. 26, 53-62 (1991; Zbl 0645.08004), the reviewer proved that the class of lattices of equational theories of unary algebras including non-regular equational theories is the class of congruence lattices of monoids with left (or right) zero. Let \(\mathcal M\) be a monoid, \(\langle A,\circ\rangle\) be the monoid obtained from \(\mathcal M\) by means of free addition of left zero \(\omega\), \(h\) be a unary operation on \(A\) such that \(h(a)= h(a\omega)= a\) for any \(a\) from \(\mathcal M\). From the results of the mentioned paper, it follows immediately that the class of congruence lattices of all such algebras \({\mathcal M}(h)=\langle A,\circ,h\rangle\) is the class of lattices of equational theories of unary algebras. In the reviewed paper it is proved that the class of lattices of equational theories of universal algebras is included in the class of congruence lattices of monoids with one additional unary operation.
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 20M99
zbMATH DE Number: 203149
zbMATH Keywords: monoid
zbMATH Keywords: congruence lattices
zbMATH Keywords: lattices of equational theories
MaRDI profile type: Publication
cites work: A property of the lattice of equational theories
full work available at URL: https://doi.org/10.1007/bf01196092
OpenAlex ID: W2085771336
description: scientific article; zbMATH DE number 203149