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Notes on sectionally complemented lattices. IV How far does the Atom Lemma go?
- Source :
- Acta Mathematica Hungarica. 117:41-60
- Publication Year :
- 2007
- Publisher :
- Springer Science and Business Media LLC, 2007.
-
Abstract
- There are two results in the literature that prove that the ideal lattice of a finite, sectionally complemented, chopped lattice is again sectionally complemented. The first is in the 1962 paper of G. Gratzer and E. T. Schmidt, where the ideal lattice is viewed as a closure space to prove that it is sectionally complemented; we call the sectional complement constructed then the 1960 sectional complement. The second is the Atom Lemma from a 1999 paper of the same authors that states that if a finite, sectionally complemented, chopped lattice is made up of two lattices overlapping in an atom and a zero, then the ideal lattice is sectionally complemented.
Details
- ISSN :
- 15882632 and 02365294
- Volume :
- 117
- Database :
- OpenAIRE
- Journal :
- Acta Mathematica Hungarica
- Accession number :
- edsair.doi...........507a961398d904f083b2f88985f7d02d