文章基本信息

标题：Pseudocomplementation on the Lattice of Convex Sublattices of a Lattice
其他标题：Pseudocomplementation on the Lattice of Convex Sublattices of a Lattice
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：1
页码：87-90
DOI：10.3329/jsr.v2i1.2485
语种：English
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：Mathematics;Upper continuous lattice; Pseudocomplemented lattice; Dense lattice; Stone lattice.