Lattice Theory

9400511国家这项研究是关于有限格的方程理论和自由格的结构的研究。这些问题是相关的，因为关于晶格簇的问题通常可以解释为自由晶格中的问题。这项工作的第一个目标是确定哪些有限生成的格的方程类具有项重写系统。第二个目标是找到一种算法来确定覆盖给定有限生成格簇的所有格簇。主要研究者还将研究哪些有序集可以嵌入到自由格中，以及哪些格是自由格的子格。格是离散的数学对象，其结构在某种程度上反映了集合论或逻辑的结构。这种非常弱的结构意味着格子可以在许多数学环境中找到。这也意味着问题很容易陈述，很难解决，而且具有非常普遍的性质。这项工作的成果将对数学、计算机科学、社会科学和企业管理的许多领域产生影响。

9400511 Nation This research is concerned with the study of the equational theory of finite lattices and the structure of free lattices. These problems are related because questions about lattice varieties can often be interpreted as problems in free lattices. The first objective of this work is to determine which finitely generated equational classes of lattices have a term rewrite system. The second objective is to find an algorithm for determining all lattice varieties which cover a given finitely generated lattice variety. The principal investigator will also study which ordered sets can be embedded in free lattices, and which lattices are sublattices of free lattices. Lattices are discrete mathematical objects with a structure reflecting to some extent the structure of set theory or logic. This very weak structure means that lattices can be found in many mathematical environments. It also means that problems are easy to state, hard to solve and of a very general nature. The results of this work will impact many areas of mathematics, computer science, the social sciences and business management.