Mathematical Sciences: Commutative Algebra

这个项目是关于交换 局部环上的代数及其奇点 主题包括 m-准素理想Hilbert函数和Hilbert多项式 在Cohen-Macaulay局部环中，以及双有理扩张和 完成本地域。 这项工作有具体的应用 代数几何，特别是解决 奇异性 交换环是一种代数结构， 交换加法和交换乘法。 这些 结构贯穿数学始终。 常见的例子包括 多项式环和代数整数环的扩张 理性的领域。 该项目涉及一个 关于交换环结构的各种问题。

This project is concerned with research in commutative algebra on local rings and their singularities. Topics include the Hilbert function and Hilbert polynomial of an m-primary ideal in a Cohen-Macaulay local ring, and birational extensions and completions of local domains. The work has specific applications to algebraic geometry, particularly to the problem of resolution of singularities. Commutative rings are algebraic structures possessing a commutative addition and a commutative multiplication. These structures occur throughout mathematics. 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.