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Minimal partial clones

Published online by Cambridge University Press:  17 April 2009

F. Börner ,
L. Haddad  and
R. Pöschel
F. Börner
Affiliation:
Karl-Weierstrass-Institut for Mathematics, Mohrenstrasse 39, Berlin 1086, Germany
L. Haddad
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, CanadaM5S 1A1
R. Pöschel
Affiliation:
Karl-Weierstrass-Institut for Mathematics, Mohrenstrasse 39, Berlin 1086, Germany
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Abstract

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Let A be a finite set. A partial clone on A is a composition closed set of operations containing all projections. It is well known that the partial clones on A, ordered by inclusion, form a lattice. We show that the minimal partial clones on A are:

(a) minimal clones of full operations or

(b) generated by partial projections defined on a totally reflexive and totally symmetric domain.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 3 , December 1991 , pp. 405 - 415
Copyright
Copyright © Australian Mathematical Society 1991

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