Mathematical Sciences: "Topics in Commutative Algebra"

数学科学：“交换代数专题”

• 批准号: 9101176
• 负责人: William Heinzer
• 金额: $ 9.13万
• 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: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1995-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101176&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Commutative; Algebra

This project is concerned with the following topics in commutative algebra: (1) the structure of the prime ideal spectra and the groups of invertible ideals in certain rings of integer-valued polynomials; (2) the structure of the homogeneous complete ideals in the polynomial ring kıX,Y,Z! and the connections with linear systems of curves in the projective plane; and (3) the projective line over a countable 1- dimensional local domain R and the structure of the spectra of integral domains between the polynomial ring RıX! and its field of fractions. Commutative rings are algebraic structures possessing a commutative addition and a commutative multiplication. These structures occur throughout mathematics and algebra. Common examples include polynomial rings, and rings of algebraic integers in extension fields of the rationals. This project is conerned with a variety of questions on the structure of commutative rings.

该项目涉及以下主题， 交换代数：（1）素理想谱的结构 和某些环中的可逆理想群 （2）齐次多项式的结构; 多项式环kiX，Y，Z中的完全理想和连接 （3）在射影平面上的线性曲线系; 可列1维局部域R上的投影线，以及 积分域之间的谱的结构， 多项式环RıX！和它的分数场 交换环是一种代数结构， 交换加法和交换乘法。 这些 结构贯穿数学和代数。 共同 例子包括多项式环和代数整数环 在有理数的扩张域中。 这个项目是conerned 关于交换环结构的各种问题。