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Complementary closed relational clones are not always Krasner clones |
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| Authors: | M Droste D Kuske R McKenzie R Pöschel |
| Institution: | Technische Universit?t Dresden, Institut fur Algebra, D-01062 Dresden, Germany, e-mail: droste@math.tu-dresden.de, poeschel@math.tu-dresden.de, GE Deptartment of Mathematics and CS, University of Leicester, Leicester LE1 7RH, England, e-mail: d.kuske@mcs.le.ac.uk, UK Vanderbilt University, 1326 Stevens Center, Nashville, Tennessee 37240, USA, e-mail: mckenzie@math.vanderbilt.edu, US |
| Abstract: | In ZFC, it is shown that every relational clone on a set A closed under complementation is a Krasner clone if and only if A is at most countable. This is achieved by solving an equivalent problem on locally invertible monoids: A partially ordered set is constructed whose endomorphism monoid is not contained in the local closure of its automorphism group. Received September 5, 1998; accepted in final form December 10, 1998. |
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