Chains of modular elements and lattice connectivity
It is well-known that if a finite lattice \(L\) possesses a maximal chain \(0<m_1<m_2<\cdots<m_r<1\) in which all elements \(m_i\), \( i=1,2,\dots,r\), are modular, then its order complex is at least \((r-2)\)-connected. The goal of the present note is to generalize the above result. Its main theorem (Theorem 1) shows that the conclusion remains valid without the assumption that the considered chain is maximal.
scientific article; zbMATH DE number 5146179
scientific article