학술저널
NOTES ON MODULAR ORDERED SETS
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 25, No. 1
-
2012.02105 - 113 (9 pages)
- 4
Generalizing modular lattices, a concept of modular ordered sets was introduced by Chajda and Rachunek. In this pa- per, we characterize modular ordered sets as those partially ordered set P satisfying that for a; b; c 2 P with b · c, l(a; b) = l(a; c) and u(a; b) = u(a; c) imply b = c. Using this, we obtain a su±- cient condition for them. We also discuss the modularity of the Dedekind-MacNeille completions of ordered sets.
1. Introduction
2. Modular ordered sets
3. Dedekind-MacNeille completions of ordered sets
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