U.S.-Australian Cooperative Research: Categories, Languages and Completely Regular Semigroup Varieties

美澳合作研究：类别、语言和完全正则半群簇

• 批准号: 8913404
• 负责人: Peter Jones
• 金额: $ 0.93万
• 依托单位: Marquette University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-15 至 1994-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8913404&HistoricalAwards=false
• 关键词: U.S.; Australian; Cooperative; Research; Categories

This award supports a visit by Dr. Peter R. Jones of Marquette University to the University of Tasmania, in Hobart, to work with Dr. Peter G. Trotter on an area of number theory involving semigroups. The investigators plan to merge two areas of semigroup theory research which have seen the greatest advances over the past decade, but whose development has been almost completely independent. The first is "finite" semigroup theory, which arises from the explicit connections among formal languages, automata and finite semigroups. The other is the theory of completely regular semigroups--those which are unions of their subgroups, and research on which has seen a resurgence of late. Important recent developments in each field will be applied to the other, notably Polak's decomposition theory for varieties will be applied to finite semigroup theory, and the "derived category" of a morphism will be applied to completely regular semigroup theory. The key fusion will involve a systematic study of the "local" varieties of completely regular monoids.

该奖项支持Peter R.的琼斯 马奎特大学到塔斯马尼亚大学，在 霍巴特，与彼得G。小跑在一个地区， 包含半群的数论 调查人员 计划合并半群理论研究的两个领域 在过去， 十年，但其发展几乎 完全独立 一是“有限” 半群理论，它产生于明确的 形式语言、自动机和有限 半群 另一种是完全的理论 正则半群--它们是 亚组，以及研究已经看到了复苏 晚了 每个领域最近的重要发展 将被应用于另一个，特别是波拉克的 分解理论的品种将适用于 有限半群理论，以及 一个态射将被应用于完全正则 半群理论 密钥融合将涉及一个 系统研究“地方”品种的完全 正则幺半群