Mathematical Sciences: Universal Algebra and Lattice Theory

数学科学：通用代数和格论

• 批准号: 8901756
• 负责人: Ralph Freese
• 金额: $ 7.96万
• 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: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901756&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Universal; Algebra; Lattice

This project is concerned with the study of basic problems in universal algebra and lattice theory. The specific areas of investigation will be the study of the complexity of certain algorithms in finitely presented lattices; modular congruence varieties; the determination of a common generalization to Ore's and Jonsson's theorems on direct decompositions; development of a computer algebra system dealing with finitely presented lattices; and projective planes over prime fields. 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, difficult to solve and of a very general nature.

这个项目是关于基本问题的研究 在泛代数和格理论中。的具体领域 调查将是对某些复杂性的研究 模表示格算法;模同余;模同余 品种;确定一个共同的概括， Ore和Jonsson关于直接分解的定理; 计算机代数系统的研制 提出格;和素域上的射影平面。 格是离散的数学对象，具有 结构在某种程度上反映了集合论的结构 或逻辑。这种非常弱的结构意味着晶格可以 在许多数学环境中发现。这也意味着 问题说起来容易，解决起来难， 一般性质。