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NOTES ON MODULAR ORDERED SETS
- Authors
- 신선호
- Issue Date
- Feb-2012
- Publisher
- 충청수학회
- Keywords
- modular ordered sets; Dedekind-MacNeille completions
- Citation
- 충청수학회지, v.25, no.1, pp.105 - 114
- Journal Title
- 충청수학회지
- Volume
- 25
- Number
- 1
- Start Page
- 105
- End Page
- 114
- ISSN
- 1226-3524
- Abstract
- Generalizing modular lattices, a concept of modular ordered sets was introduced by Chajda and Rachunek. In this paper, we characterize modular ordered sets as those partially ordered set $P$ satisfying that for $a, b, c \in P$ with $b \leq c$, $l(a, b)=l(a, c)$ and $u(a, b)=u(a, c) $ imply $b=c$. Using this, we obtain a sufficient condition for them. We also discuss the modularity of the Dedekind-MacNeille completions of ordered sets.
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