Lattice Theory

格子理论

• 批准号: 9400511
• 负责人: James Nation
• 金额: $ 7.5万
• 依托单位: University of Hawaii
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400511&HistoricalAwards=false
• 关键词: Lattice; Theory

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.

9400511 民族 本文主要研究有限格的方程理论和自由格的结构。 这些问题是相关的，因为关于格簇的问题通常可以解释为自由格中的问题。 这项工作的第一个目标是确定哪些有限生成的格方程类具有项重写系统。 第二个目标是找到一个算法，用于确定所有的格品种，涵盖了一个给定的生成格品种。 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可以在许多数学环境中找到。 这也意味着问题容易陈述，难以解决，并且具有非常普遍的性质。 这项工作的结果将影响数学，计算机科学，社会科学和企业管理的许多领域。