Pseudocomplementation on the Lattice of Convex Sublattices of a Lattice
Keywords:Upper continuous lattice, Pseudocomplemented lattice, Dense lattice, Stone lattice.
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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