Abe, Tetsuya Strong semimodular lattices and Frankl’s conjecture. (English) Zbl 1013.06008 Algebra Univers. 44, No. 3-4, 379-382 (2000). Frankl’s conjecture says that in every nontrivial finite lattice \(L\) there is a join-irreducible element \(a\) such that the principal filter \(F(a)\) has at most \(|L|/2\) elements. It is known that this conjecture holds for lower semimodular or section-complemented lattices, but it is unknown whether it holds for upper semimodular lattices. The author introduces the concept of a strong semimodular lattice and proves Frankl’s conjecture for these lattices. Reviewer: Ivan Chajda (Olomouc) Cited in 10 Documents MSC: 06C10 Semimodular lattices, geometric lattices 06C15 Complemented lattices, orthocomplemented lattices and posets Keywords:strong semimodular lattice; Frankl’s conjecture PDFBibTeX XMLCite \textit{T. Abe}, Algebra Univers. 44, No. 3--4, 379--382 (2000; Zbl 1013.06008) Full Text: DOI