On the local closure of clones on countable sets

Erhard Aichinger

doi:10.1007/s00012-017-0465-9

On the local closure of clones on countable sets

Erhard Aichinger

Institute for Algebra

Research output: Contribution to journal › Article › peer-review

Abstract

We consider clones on countable sets. If such a clone has quasigroup operations, is locally closed and countable,then there is a function $f : \N \to \N$ such that the $n$-ary part of $C$ is equal to the $n$-ary part of $\Pol \Inv^{[f(n)]} C$, where $\Inv^{[f(n)]} C$ denotes the set of $f(n)$-ary invariant relations of $C$.

Original language	English
Pages (from-to)	355-361
Number of pages	7
Journal	Algebra Universalis
Volume	78
Issue number	3
DOIs	https://doi.org/10.1007/s00012-017-0465-9
Publication status	Published - 2017

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101013 Mathematical logic
102031 Theoretical computer science

JKU Focus areas

Computation in Informatics and Mathematics
Engineering and Natural Sciences (in general)

Access to Document

10.1007/s00012-017-0465-9

Cite this

@article{e49713922c8448779589e5799d27056d,

title = "On the local closure of clones on countable sets",

abstract = "We consider clones on countable sets. If such a clone has quasigroup operations, is locally closed and countable,then there is a function \$f : \textbackslash{}N \textbackslash{}to \textbackslash{}N\$ such that the \$n\$-ary part of \$C\$ is equal to the \$n\$-ary part of \$\textbackslash{}Pol \textbackslash{}Inv\textasciicircum{}\{[f(n)]\} C\$, where \$\textbackslash{}Inv\textasciicircum{}\{[f(n)]\} C\$ denotes the set of \$f(n)\$-ary invariant relations of \$C\$.",

author = "Erhard Aichinger",

year = "2017",

doi = "10.1007/s00012-017-0465-9",

language = "English",

volume = "78",

pages = "355--361",

journal = "Algebra Universalis",

issn = "0002-5240",

publisher = "Springer Basel AG 2011",

number = "3",

}

TY - JOUR

T1 - On the local closure of clones on countable sets

AU - Aichinger, Erhard

PY - 2017

Y1 - 2017

N2 - We consider clones on countable sets. If such a clone has quasigroup operations, is locally closed and countable,then there is a function $f : \N \to \N$ such that the $n$-ary part of $C$ is equal to the $n$-ary part of $\Pol \Inv^{[f(n)]} C$, where $\Inv^{[f(n)]} C$ denotes the set of $f(n)$-ary invariant relations of $C$.

AB - We consider clones on countable sets. If such a clone has quasigroup operations, is locally closed and countable,then there is a function $f : \N \to \N$ such that the $n$-ary part of $C$ is equal to the $n$-ary part of $\Pol \Inv^{[f(n)]} C$, where $\Inv^{[f(n)]} C$ denotes the set of $f(n)$-ary invariant relations of $C$.

UR - https://www.scopus.com/pages/publications/85031940680

U2 - 10.1007/s00012-017-0465-9

DO - 10.1007/s00012-017-0465-9

M3 - Article

SN - 0002-5240

VL - 78

SP - 355

EP - 361

JO - Algebra Universalis

JF - Algebra Universalis

IS - 3

ER -

On the local closure of clones on countable sets

Abstract

Fields of science

JKU Focus areas

Access to Document

Other files and links

Clonoids: a unifying approach to equational logic and clones

Cite this

On the local closure of clones on countable sets

Abstract

Fields of science

JKU Focus areas

Access to Document

Other files and links

Projects

Clonoids: a unifying approach to equational logic and clones

Cite this