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Discussiones Mathematicae General Algebra and Applications 21(1) (2001) 5-11
DOI: https://doi.org/10.7151/dmgaa.1022

THE SŁUPECKI CRITERION BY DUALITY

Eszter K. Horváth

Bolyai Institute, University of Szeged
Aradi vértanúk tere 1, H-6720 Szeged, Hungary
e-mail: horeszt@math.u-szeged.hu

Abstract

A method is presented for proving primality and functional completeness theorems, which makes use of the operation-relation duality. By the result of Sierpiński, we have to investigate relations generated by the two-element subsets of A^k only. We show how the method applies for proving Słupecki's classical theorem by generating diagonal relations from each pair of k-tuples.

Keywords: primal algebra, diagonal relation, Galois connection, Słupecki Criterion.

2000 Mathematics Subject Classification: 08A02, 08A40, 08A62, 06A15.

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Received 9 February 1998
Revised 6 November 2000
Revised 5 March 2001