论文标题
一致的晶格和纤细半模块晶格的灯的笔记
Notes on congruence lattices and lamps of slim semimodular lattices
论文作者
论文摘要
自从G.Grätzer和E. Knapp于2007年引入以来，已有四个以上的论文专门用于有限的Slim Slim平面半模块化晶格（简而言之，SPS Lattices或Slim Slim Semimindimpular Lattices）和一些相关领域。除了分配性外，这些晶格的一致性晶格还有七个已知特性。前两个物业由G.Grätzer证明了下四个物业，由本作者证明，而G.Grätzer和现任作者共同证明了第七座。在七个属性中，有五个属性通过使用灯找到并证明了这是本作者在2021年论文中引入的晶格理论工具。在这里，使用灯，我们提供了无限的许多新属性。灯也使我们能够加强先前已知的第七个属性，并导致指数时间的算法来决定是否可以将有限的分布晶格表示为SPS晶格的一致性晶格。还给出了一些灯的新属性。
Since their introduction by G. Grätzer and E. Knapp in 2007, more than four dozen papers have been devoted to finite slim planar semimodular lattices (in short, SPS lattices or slim semimodular lattices) and to some related fields. In addition to distributivity, there have been seven known properties of the congruence lattices of these lattices. The first two properties were proved by G. Grätzer, the next four by the present author, while the seventh was proved jointly by G. Grätzer and the present author. Five out of the seven properties were found and proved by using lamps, which are lattice theoretic tools introduced by the present author in a 2021 paper. Here, using lamps, we present infinitely many new properties. Lamps also allow us to strengthen the seventh previously known property, and they lead to an algorithm of exponential time to decide whether a finite distributive lattice can be represented as the congruence lattice of an SPS lattice. Some new properties of lamps are also given.
