文章基本信息
- 标题：Pseudocomplementation on the Lattice of Convex Sublattices of a Lattice
- 本地全文：下载
- 作者：R. M. H. Rahman
- 期刊名称：Journal of Scientific Research
- 印刷版ISSN：2070-0237
- 电子版ISSN：2070-0245
- 出版年度：2010
- 卷号：2
- 期号：01
- 页码：87-90
- DOI：10.3329/jsr.v2i1.2485
- 出版社：Rajshahi University
- 摘要：
By a new partial ordering relation "≤" the set of convex sublattices CS(L) of a lattice L is again a lattice. In this paper we establish some results on the pseudocomplementation of (CS(L); ≤). We show that a lattice L with 0 is dense if and only if CS(L) is dense. Then we prove that a finite distributive lattice is a Stone lattice if and only if CS(L) is Stone. We also prove that an upper continuous lattice L is a Stone lattice if and only if CS(L) is Stone.
Keywords : Upper continuous lattice; Pseudocomplemented lattice; Dense lattice; Stone lattice.
© 2010 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.
DOI: 10.3329/jsr.v2i1.2485 J. Sci. Res. 2 (1), 87-90 (2010)
- 关键词：Upper continuous lattice
