Mathematical Sciences: Decompositions of Cohen Macaulay Modules

本文研究交换代数中的两个问题。首席研究员将分析Cohen-Macaulay模块的直接和分解。她还将研究诺瑟环上素数理想的部分有序集的结构以及这个偏序集对环上模的直接和行为的影响。交换环是具有交换加法和交换乘法的代数结构。这些结构贯穿于数学和代数。常见的例子包括多项式环和有理数扩展域中的代数整数环。本课题涉及交换环的几个问题。

This research is concerned with two problems in commutative algebra. The principal investigator will analyze the direct-sum decompositions of Cohen-Macaulay modules. She will also study the structure of the partially ordered set of prime ideals in a noetherian ring and the influence of this poset on the direct-sum behavior of modules over the ring. 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 concerned with several questions concerning commutative rings.