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：
暂无
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.
引用
收藏
页码：421 / 431
页数：10
相关论文
共 50 条
  • [41] POSETS FOR CONFIGURATIONS
    RENSINK, A
    LECTURE NOTES IN COMPUTER SCIENCE, 1992, 630 : 269 - 285
  • [42] On multipartite posets
    Agnarsson, Geir
    DISCRETE MATHEMATICS, 2008, 308 (22) : 5284 - 5288
  • [43] Tchebyshev posets
    Hetyei, G
    DISCRETE & COMPUTATIONAL GEOMETRY, 2004, 32 (04) : 493 - 520
  • [44] Partitioning posets
    Patel, Viresh
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2008, 25 (02): : 131 - 152
  • [45] Hypercontinuous posets
    Wenfeng Zhang
    Xiaoquan Xu
    Chinese Annals of Mathematics, Series B, 2015, 36 : 195 - 200
  • [46] Representable posets
    Egrot, Rob
    JOURNAL OF APPLIED LOGIC, 2016, 16 : 60 - 71
  • [47] Cayley Posets
    Garcia-Marco, Ignacio
    Knauer, Kolja
    Mercui-Voyant, Guillaume
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2020, 17 (06)
  • [48] Independence posets
    Thomas, Hugh
    Williams, Nathan
    JOURNAL OF COMBINATORICS, 2019, 10 (03) : 545 - 578
  • [49] REALIZABLE POSETS
    PIERCE, RS
    VINSONHALER, C
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 1990, 7 (03): : 275 - 282
  • [50] STABILITY AND POSETS
    Jockusch, Carl G., Jr.
    Kastermans, Bart
    Lempp, Steffen
    Lerman, Manuel
    Solomon, Reed
    JOURNAL OF SYMBOLIC LOGIC, 2009, 74 (02) : 693 - 711
12345