Pseudocomplementation on the Lattice of Convex Sublattices of a Lattice

Authors

  • R. M. H. Rahman Dinajpur Govt College, Bangladesh

DOI:

https://doi.org/10.3329/jsr.v2i1.2485

Keywords:

Upper continuous lattice, Pseudocomplemented lattice, Dense lattice, Stone lattice.

Abstract

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)

 

Downloads

Download data is not yet available.
Abstract
94
PDF
89

Author Biography

R. M. H. Rahman, Dinajpur Govt College, Bangladesh

Associate Professor, Department of Mathematics

Dinajpur Govt. College, Dinajpur

Downloads

Published

2009-12-26

How to Cite

Rahman, R. M. H. (2009). Pseudocomplementation on the Lattice of Convex Sublattices of a Lattice. Journal of Scientific Research, 2(1), 87–90. https://doi.org/10.3329/jsr.v2i1.2485

Issue

Vol. 2 No. 1 (2010)

Section

Section A: Physical and Mathematical Sciences

License

© Journal of Scientific Research

Creative Commons License

Articles published in the "Journal of Scientific Research" are Open Access articles under a Creative Commons Attribution-ShareAlike 4.0 International license (CC BY-SA 4.0). This license permits use, distribution and reproduction in any medium, provided the original work is properly cited and initial publication in this journal. In addition to that, users must provide a link to the license, indicate if changes are made and distribute using the same license as original if the original content has been remixed, transformed or built upon.