Uniquely Complemented Posets

被引：0
|
作者：
Ivan Chajda
Helmut Länger
Jan Paseka
机构：
[1] Palacký University Olomouc,Faculty of Science, Department of Algebra and Geometry
[2] Institute of Discrete Mathematics and Geometry,Faculty of Mathematics and Geoinformation
[3] Masaryk University Brno,Faculty of Science, Department of Mathematics and Statistics
来源：
Order | 2018年 / 35卷
关键词：
Complemented poset; Uniquely complemented; Atomic; Atomistic; Distributive; LU-identity;
D O I：
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中图分类号：
学科分类号：
摘要：
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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页码：421 / 431
页数：10
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