Mathematical Sciences: Topics in Commutative Algebra

Heinzer 9622224 这一建议支持W.海因策工作的问题交换代数。他打算研究一个局部域和它的完成之间的中间环。他还打算研究结构的理想在一个二维经常当地环，衍生物的总理理想在无限积分扩展，收缩的理想从一维overrings与应用主要分解的权力理想在诺特环，和内容的高斯多项式。 本文的研究是在交换代数与代数几何的边界上进行的。这两个领域产生于经典的问题，研究数学对象定义在平面上的最简单的方程，即多项式。今天，这些领域不仅使用代数方法，而且还使用分析和拓扑学方法，相反，这些领域广泛使用。 此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人学等不同领域都很有用。

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.