2 problems

Let $L$ be a modular lattice, and let $\sigma$ be a linear extension of $L$. For $x\in L$, write $\operatorname{Cov}_L^{\uparrow}(x)$ for the elements covering $x$ and…

Let $P$ be an upho modular lattice, meaning that $P$ is of finite type and its principal order filter at every element is isomorphic to $P$. Suppose that $P$ is indecomposable and…