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)

 

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Author Biography

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

Associate Professor, Department of Mathematics

Dinajpur Govt. College, Dinajpur

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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

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Section

Section A: Physical and Mathematical Sciences