Mathematical Sciences: Topics in Commutative Ring Theory

数学科学：交换环理论主题

• 批准号: 8800762
• 负责人: William Heinzer
• 金额: $ 11.15万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-01 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8800762&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Commutative; Ring

This research concerns work on the following topics in the area of commutative associative rings and algebras. The first is birational normal spots and exceptional prime divisors over a 2- dimensional normal local domain. A specific question here is whether a 2-dimensional normal local domain that satisfies Muhly's condition (N) necessarily has torsion divisor class group. The second topic concerns finite generation of ideals contracted from a polynomial ring extension. An interesting question in this area is whether a 1-dimensional coherent domain has the property that its integral closure is a Prufer domain. The third topic concerns ring and field extensions that are not finitely generated but have the property that each proper subextension is finitely generated. Other topics in commutative ring theory concerned with the behavior of the Picard group under ring extension, the structure of rings of interest in control theory, and the multiplicity of adjacent ideals in a 2- dimensional regular local domain will be considered. Commutative rings are algebraic structures possessing a commutative addition and a commutative multiplication. These structures occur throughout mathematics and algebra and common examples include polynomial rings, and rings of algebraic integers in extension fields of the rationals. This project is concerned with a variety of questions on the structure of commutative rings.

这项研究涉及以下主题的工作， 交换结合环和代数的面积。一是 双有理正规点和例外素因子 维正规局域这里的一个具体问题是 是否一个二维正常的局部域，满足 Muhly条件（N）必有挠因子类 组第二个主题是关于理想的有限生成 从多项式环扩展收缩。一个有趣 这个领域的问题是，一个一维相干域 具有积分闭包是Prufer整环的性质。 第三个主题是关于环和域的扩展， 生成的，但具有每个适当的 子扩展将自动生成。交换式中的其他主题 关于Picard群的行为的环理论， 环的扩展，对环的结构感兴趣的控制 理论，和相邻理想的多重性在一个2- 将考虑三维规则局部域。 交换环是一种代数结构， 交换加法和交换乘法。这些 结构出现在数学和代数中， 例子包括多项式环和代数环。 在有理数的扩张域中的整数。这个项目是 关于结构的各种问题， 交换环