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Reconstruction of Finite Truncated Semi-Modular Lattices

✍ Scribed by Jean-Xavier Rampon; Bernd S.W. Schröder

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 194 KB
Volume: 86
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.2002.2126

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✦ Synopsis

In this paper, we prove reconstruction results for truncated lattices. The main results are that truncated lattices that contain a 4-crown and truncated semi-modular lattices are reconstructible. Reconstruction of the truncated lattices not covered by this work appears challenging. Indeed, the remaining truncated lattices possess very little lattice-typical structure. This seems to indicate that further progress on the reconstruction of truncated lattices is closely correlated with progress on reconstructing ordered sets in general. # 2002 Elsevier Science (USA) MSC: 06A07.

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A Representation of Finitely-Modular AC-lattices

✍ Jan Hamhalter 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 231 KB

## Abstract We give a lattice‐theoretic characterization of the lattices of Mackey closed subspaces in a vector space __V__ (dim __V__ ≧ 4): These are exactly complete finitely‐modular AC‐lattices of the length at least four which have mutually perspective atoms.