NOTES ON MODULAR ORDERED SETS

• 발행기관: 충청수학회
• 저자명: Seon Ho Shin
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 25, No. 1, 105~113쪽, 전체 9쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2012.02.28

영문 초록

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.

목차

1. Introduction

2. Modular ordered sets

3. Dedekind-MacNeille completions of ordered sets