Some results on semimodular lattices. (English) Zbl 1236.06003

Czédli, Gábor; Schmidt, E. Tamás

Chajda, I. (ed.) et al., Proceedings of the 79th workshop on general algebra “79. Arbeitstagung Allgemeine Algebra”, 25th conference of young algebraists, Palacký University Olomouc, Olomouc, Czech Republic, February 12–14, 2010. Klagenfurt: Verlag Johannes Heyn (ISBN 978-3-7084-0407-3/pbk). Contributions to General Algebra 19, 45-56 (2010).

Authors’ abstract: “Some recent results on semimodular lattices are surveyed, and some related results are given. The topics include a strong form of the Jordan-Hölder theorem, the semimodularity of subdirect products, representations as cover-preserving join-homomorphic images of distributive lattices, cover-preserving embeddings into geometric lattices, and the congruence lattices of finite almost-geometric lattices.”
The main new results concern semimodular lattices of sectionally finite length as homomorphic images.
For the entire collection see [Zbl 1201.08001].

Reviewer: Jan Jakubík (Košice)

MSC:

06C10	Semimodular lattices, geometric lattices
06B15	Representation theory of lattices

Keywords:

semimodular lattice; geometric lattice; cover-preserving embedding