Mathematical Sciences: Research in Ring Theory

数学科学：环理论研究

• 批准号: 9301244
• 负责人: Kenneth Goodearl
• 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: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9301244&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Ring; Theory

This award supports research in the general area of noncommutative ring theory. The principal investigator will investigate the structure of skew polynomial rings, quantum coordinate algebras, noetherian rings, and related rings. This research is in the general area of ring theory. A ring is an algebraic object having both an addition and a multiplication defined on it. Although the additive operation satisfies the commutative law, the multiplicative operation is not required to do so. An example of a ring for which multiplication is not commutative is the collection of nxn matrices over the integers. The study of noncommutative rings has become an important part of algebra because of its increasing significance to other branches of mathematics and physics.

该奖项支持非交换环理论一般领域的研究。首席研究员将研究歪斜多项式环、量子坐标代数、诺etherian环和相关环的结构。本研究属于环理论的一般范畴。环是一个代数对象，在它上面定义了加法和乘法。虽然加法运算满足交换律，但乘法运算不需要满足交换律。一个乘法不可交换的环的例子是整数上的nxn个矩阵的集合。非交换环的研究由于其对其他数学和物理分支的重要意义而成为代数的重要组成部分。