Mathematical Sciences: Finite Dimensional Algebras and Artinian Rings

数学科学：有限维代数和阿天环

• 批准号: 9002498
• 负责人: Birge Huisgen-Zimmermann
• 金额: --
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002498&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Finite; Dimensional; Algebras

This project is concerned with various aspects of artinian rings, in particular homological properties of finite dimensional algebras and decomposition properties of modules. In the first category, the goal is to obtain a better understanding of global and finitistic dimensions. Under the second, the aim is to obtain a representation theory for rings all of whose left modules are direct sums of finitely generated components. The research is in the general area of ring theory. A ring is an algebraic structure having both an addition and a multiplication defined on it. These objects arise naturally and are important in many areas of mathematics and physics.

这个项目涉及到Artin环的各个方面，特别是有限维代数的同调性质和模的分解性质。在第一类中，目标是更好地了解全球层面和有限层面。在第二种情形下，目的是得到左模都是有限生成分支的直和的环的表示理论。这项研究属于环论的一般领域。环是定义了加法和乘法的代数结构。这些物体是自然产生的，在数学和物理的许多领域都很重要。