Maximal partial clones with no finite basis
type: Item
instance of: scholarly article
title: Maximal partial clones with no finite basis
zbMATH Open document ID: 0936.08004
author: Yanyan Li
published in: Algebra Universalis
publication date: 2000-02-27T00:00:00Z
review text: E. Post described all clones on a 2-element set \(A\) and showed that every of these clones is finitely generated. This result does not hold for \(|A|\geq 3\). However, R. Freivalds has constructed a partial clone (i.e., a superposition closed subset of partial functions on \(A\) containing all projections) on a 2-element set which is not finitely generated. A partial clone is called strong if it contains all subfunctions of its partial functions. The authors give a criterion for recognizing not finitely generated strong partial clones and show that among all \(|A|+ 1\) maximal partial clones of Slupiecki type on \(A\), only one is finitely generated.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 08A55
zbMATH DE Number: 1407117
zbMATH Keywords: partial clone
zbMATH Keywords: finitely generated clone
zbMATH Keywords: Slupiecki clone
MaRDI profile type: Publication
full work available at URL: s000120050095
OpenAlex ID: W2051562247
DOI: 10.1007/S000120050095
description: scientific article; zbMATH DE number 1407117