论文标题
矩形晶格的矩形间隔是矩形晶格
A rectangular interval of a rectangular lattice is a rectangular lattice
论文作者
论文摘要
令$ l $为苗条，平面，半模块晶格（Slim表示它不包含$ {\ Mathsf M} _3 $ -Sublattices）。 We call the interval $I = [o, i]$ of $L$ \emph{rectangular}, if there are $u_l, u_r \in [o, i] - \{o,i\}$ such that $o = u_l \wedge u_r$ and $i = u_l \vee u_r$, where $u_l$ is to the left of $u_r$. 我们证明矩形晶格的矩形间隔是矩形晶格。 作为应用程序，我们获得了G.Czédli的最新结果。
Let $L$ be a slim, planar, semimodular lattice (slim means that it does not contain ${\mathsf M}_3$-sublattices). We call the interval $I = [o, i]$ of $L$ \emph{rectangular}, if there are $u_l, u_r \in [o, i] - \{o,i\}$ such that $o = u_l \wedge u_r$ and $i = u_l \vee u_r$, where $u_l$ is to the left of $u_r$. We prove that a rectangular interval of a rectangular lattice is a rectangular lattice. As an application, we get a recent result of G. Czédli.
