Binary homomorphisms and natural dualities |
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Authors: | DM ClarkBA Davey JG Pitkethly |
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Institution: | a SUNY, New Paltz, NY 21561, USA b La Trobe University, Victoria 3086, Australia |
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Abstract: | We investigate ways in which certain binary homomorphisms of a finite algebra can guarantee its dualisability. Of particular interest are those binary homomorphisms which are lattice, flat-semilattice or group operations. We prove that a finite algebra which has a pair of lattice operations amongst its binary homomorphisms is dualisable. As an application of this result, we find that every finite unary algebra can be embedded into a dualisable algebra. We develop some general tools which we use to prove the dualisability of a large number of unary algebras. For example, we show that the endomorphisms of a finite cyclic group are the operations of a dualisable unary algebra. |
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Keywords: | Primary 08C15 secondary 18A40 06D50 |
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