On \(n\)-clone extensions of algebras
type: Item
instance of: scholarly article
title: On \(n\)-clone extensions of algebras
zbMATH Open document ID: 0935.08001
published in: Algebra Universalis
publication date: 2000-02-27T00:00:00Z
review text: An identity \(\varphi \approx \psi \) is clone compatible if either \(\varphi \) and \(\psi \) are the same variable or the sets of fundamental operations in \(\varphi \) and \(\psi \) are nonempty and identical. The author constructs an \(n\)-clone extension of a given algebra and for a variety \(V\) he denotes by \(V^c\) the variety defined by all clone compatible identities from Id\((V)\) and by \(V^{c,n}\) the \(n\)-clone extension of \(V\). The paper contains representations of algebras from \(V^c\) and \(V^{c,n}\) under certain assumptions. The results are applied to several important varieties including the variety of distributive lattices and the variety of Boolean algebras.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08A05
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 08B05
zbMATH DE Number: 1407100
zbMATH Keywords: clone extension
zbMATH Keywords: clone compatible identities
zbMATH Keywords: variety of algebras
author: Jerzy Płonka
MaRDI profile type: Publication
full work available at URL: s000120050078
OpenAlex ID: W2306602302
DOI: 10.1007/S000120050078
description: scientific article; zbMATH DE number 1407100