On the structure and representation of clones
type: Item
instance of: scholarly article
title: On the structure and representation of clones
zbMATH Open document ID: 0636.08003
DOI: 10.1007/BF01229963
author: Arturo Sangalli
published in: Algebra Universalis
publication date: 1988-01-01T00:00:00Z
review text: Let C be an abstract clone. We define an equivalence relation on C and show that C is isomorphic to the clone \(\hat C\) of all operations on the quotient set \(X_ C\) preserved by a monoid \(M_ C\) of transformations of \(X_ C\). It turns out that \(<X_ C,\hat C>\) is a countably generated free algebra and \(M_ C\) is the monoid generated by those endomorphisms which fix all but one generator. As an application we prove that all endomorphism monoids and automorphism groups of finite powers of algebras arise, up to isomorphism, from unary algebras.
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 08A35
Mathematics Subject Classification ID: 08A05
Mathematics Subject Classification ID: 08A60
zbMATH DE Number: 4035897
zbMATH Keywords: transformation monoid
zbMATH Keywords: clone
zbMATH Keywords: operations
zbMATH Keywords: free algebra
zbMATH Keywords: endomorphism monoids
zbMATH Keywords: automorphism groups
zbMATH Keywords: unary algebras
MaRDI profile type: Publication
cites work: Q3950708
cites work: A representation of varieties and their morphisms
cites work: Algebras of multiplace functions
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description: scientific article; zbMATH DE number 4035897