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The join of two minimal clones and the meet of two maximal clones |
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| Authors: | Gábor Czédli Radomír Halaš Keith A. Kearnes Péter P. Pálfy Ágnes Szendrei |
| Affiliation: | (1) JATE Bolyai Institute, Szeged, Aradi Vértanúk tere 1, H-6720, Hungary, e-mail: czedli@math.u-szeged.hu, a.szendrei@math.u-szeged.hu, HU;(2) Department of Algebra and Geometry, Palacky University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail: halas@risc.upol.cz, CZ;(3) Department of Mathematics, University of Louisville, Louisville, KY 40292, USA, e-mail: kearnes@louisville.edu, US;(4) Mathematical Institute of the Hungarian Academy of Sciences, Budapest, P.O.Box 127, H-1364, Hungary, e-mail: ppp@math-inst.hu, HU |
| Abstract: | We construct two minimal clones on any finite set such that the join of the two clones contains all operations. Dually, we exhibit two maximal clones on any finite set with at least three elements such that the intersection of the two clones is the trivial clone containing projections only. Received October 20, 1998; accepted in final form December 16, 1998. |
| Keywords: | and phrases: Clone minimal clone primal algebra maximal clone. |
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