Uniquely Complemented Posets |
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| Authors: | Ivan Chajda Helmut Länger Jan Paseka |
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| Institution: | 1.Faculty of Science, Department of Algebra and Geometry,Palacky University Olomouc,Olomouc,Czech Republic;2.Faculty of Mathematics and Geoinformation,Institute of Discrete Mathematics and Geometry,Vienna,Austria;3.Faculty of Science, Department of Mathematics and Statistics,Masaryk University Brno,Brno,Czech Republic |
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| Abstract: | We study complementation in bounded posets. It is known and easy to see that every complemented distributive poset is uniquely complemented. The converse statement is not valid, even for lattices. In the present paper we provide conditions that force a uniquely complemented poset to be distributive. For atomistic resp. atomic posets as well as for posets satisfying the descending chain condition we find sufficient conditions in the form of so-called LU-identities. It turns out that for finite posets these conditions are necessary and sufficient. |
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