Mathematical Sciences: Primary Decompositions and Ajoints of Ideals

这个建议支持I. Swanson教授对交换代数问题的研究。她打算研究，在素数特征的诺瑟环中，初生分解如何随弗罗贝纽斯幂而变化。她还希望开发出计算非二维环的伴结点和核心的算法。本研究是关于交换代数与代数几何之间的边界。这两个领域都源于研究平面上由最简单的方程即多项式定义的数学对象的经典问题。今天，这些领域不仅使用代数的方法，而且还使用分析和拓扑的方法，反过来，这些方法在这些领域中被广泛使用。此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人等多种领域都很有用。

Swanson 96-23085 This proposal supports the work of Professor I. Swanson to work on problems in commutative algebra. She intends to study how, in Noetherian rings of prime characteristic, primary deomposiiton varies with Frobenius powers. She also hopes to develop algorithms for calculating adjoints and cores when the ring is not two dimensional. 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.