On algebras and clones
type: Item
instance of: scholarly article
title: On algebras and clones
zbMATH Open document ID: 0614.08004
DOI: 10.1007/BF02573092
published in: Semigroup Forum
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134858
review text: Clones of term functions are considered under the aspect of the structure of algebras. If A is an algebra, denote by T(A) the clone of term functions of A. The main topic is a mapping \(T: {\mathcal V}\to C\) from a class of algebras to the class of clones of term functions. It is shown that the class T(\({\mathcal V})\) is a \(\vee\)-sublattice of the lattice of subvarieties of the variety of clones. The clone equations are much easier to handle if they are given in the form of hyperidentities. By this method it is pointed out that the primal algebras give rise to an infinite chain of varieties in T(\({\mathcal V})\) and there are given hyperidentities for some varieties of lattices and abelian groups. For varieties in T(\({\mathcal V})\) there are found some subdirectly irreducible clones.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 08B20
zbMATH DE Number: 3993660
zbMATH Keywords: clones of term functions
zbMATH Keywords: lattice of subvarieties
zbMATH Keywords: variety of clones
zbMATH Keywords: clone equations
zbMATH Keywords: hyperidentities
zbMATH Keywords: primal algebras
zbMATH Keywords: chain of varieties
zbMATH Keywords: subdirectly irreducible clones
author: Dietmar Schweigert
MaRDI profile type: Publication
cites work: Q3934450
cites work: The lattice of interpretability types of varieties
cites work: On Malcev conditions
cites work: Q3337385
cites work: On varieties of clones
cites work: Clones of term functions of lattices and Abelian groups
cites work: Hyperidentities and hypervarieties
description: scientific article; zbMATH DE number 3993660