Mathematical Sciences: Algorithmic and Computational Methodsin Algebra

数学科学：代数中的算法和计算方法

• 批准号: 9203981
• 负责人: John Meakin
• 金额: $ 21.85万
• 依托单位: University of Nebraska-Lincoln
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-15 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203981&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algorithmic; Computational; Methodsin

This research is concerned with a study of algorithmic problems in the theories of groups, semigroups, inverse semigroups and associative algebras. Related problems about automata, varieties and pseudo-varieties will also be considered. Algorithmic problems to be considered include the word problem for non-periodic semigroup varieties, for finitely based varieties of associative algebras, for presentations and varieties of inverse semigroups. Other problems to be considered include the algorithmic classification of finitely generated subgroups of free groups via finite inverse monoids, the Rhodes problem for the class of finite groups and the extension problem for finite inverse automata to various pseudo-varieties of groups. This research is in the area of semigroups. A semigroup is one of the simplest of the abstract mathematical structures, consisting of a set with one associative operation on it. The structure of these very general objects will be investigated. Applications will be given to various areas of mathematics and computer science.

这项研究涉及的算法研究， 群、半群、逆理论中的问题 半群和结合代数。 有关问题 自动机，品种和伪品种也将被考虑。 要考虑的数学问题包括单词问题 对于非周期半群簇， 各种结合代数，用于演示和 逆半群簇 其他需要考虑的问题 包括生成的数据的算法分类 子群的自由群通过有限逆幺半群，罗兹 有限群类的扩张问题 有限逆自动机的各种伪品种的 组 这个研究是在半群的领域。 一个半群是 最简单的抽象数学结构之一 由一个具有一个关联操作的集合组成。 将研究这些非常一般的物体的结构。 应用程序将被给予数学的各个领域， 计算机科学