On pseudovarieties of monounary algebras
type: Item
instance of: scholarly article
zbMATH Open document ID: 1258.08003
DOI: 10.1142/S1793557112500039
author: Danica Jakubiková-Studenovská
published in: Asian-European Journal of Mathematics
publication date: 2012-09-03T00:00:00Z
Mathematics Subject Classification ID: 08A60
Mathematics Subject Classification ID: 08B99
zbMATH DE Number: 6075879
zbMATH Keywords: monounary algebra
zbMATH Keywords: pseudovariety
zbMATH Keywords: homomorphism
zbMATH Keywords: subalgebra
zbMATH Keywords: direct product
MaRDI profile type: Publication
cites work: On pseudovarieties
cites work: The Lattice of Equational Classes of Algebras with One Unary Operation
cites work: Topics in universal algebra
full work available at URL: s1793557112500039
OpenAlex ID: W2093363303
title: On pseudovarieties of monounary algebras
review text: Algebras with one unary operation are called monounary algebras. A class of finite algebras is called a pseudovariety if it is closed under subalgebras, homomorphic images and direct products of finitely many members. A pseudovariety \({\mathcal P}\) is called equational if there exists a variety \({\mathcal V}\) such that \({\mathcal P}\) consists of all finite members of \({\mathcal V}\). A constructive description of the members of all pseudovarieties of monounary algebras is given. That description uses finite products, homomorphisms and subalgebras. It is shown that every equational pseudovariety of monounary algebras is finitely generated; moreover, if this pseudovariety is not the pseudovariety of all monounary algebras, it can be generated by a single algebra.
reviewed by: Grigori I. Zhitomirski
description: scientific article; zbMATH DE number 6075879