Mathematical Sciences: Topics in Commutative Algebra

Heinzer 9622224这项建议支持W.Heinzer教授在交换代数中解决问题的工作。他打算研究局部环和它的完备化之间的中间环。他还打算研究二维正则局部环中理想的结构、素理想在无限积分扩张中的分支、一维上环上理想的收缩及其在Notherian环中理想幂的初等分解中的应用，以及Gauss多项式的内容。这项研究是关于交换代数和代数几何之间的边界的。这两个领域都起源于研究平面上由最简单的方程定义的数学对象的经典问题，即多项式。今天，这些领域不仅使用代数中的方法，而且还使用分析和拓扑学中的方法，相反，在这些领域中被广泛使用。此外，它在物理、理论计算机科学、密码学、编码理论和机器人学等领域都证明了自己的有用。

Heinzer 9622224 This proposal supports the work of Professor W. Heinzer to work on problems in commutative algebra. He intends to study intermediate rings between a local domain and its completion. He also intends to study the structure of ideals in a two dimensional regular local ring, the ramification of prime ideals in infinite integral extensions, the contraction of ideals from one dimensional overrings with applications to primary decomposition in powers of ideals in Noetherian rings, and the content of Gaussian polynomials. This research is on the boundary between commutative algebra and algebraic geometry. Both fields arose from the classical problem of studying mathematical objects defined in the plane by the simplest of equations, namely polynomials. Today, the fields use methods not only from algebra, but also from analysis and topology, and conversely are extensively used in those fields. Moreover it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.