Mathematical Sciences: Research in Commutative Algebra

斯里尼瓦桑9623141 这一建议支持了H.斯里尼瓦桑工作的问题交换代数。 她打算研究的多重性R/I的齐次理想我在其最小分次决议的转变。 她还打算研究有限的规定介绍了一个理想。 最后，她打算构造R/I的极小代数归结，其中I是完全归结的连接类中的理想。 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。

Srinivasan 9623141 This proposal supports the work of Professor H. Srinivasan to work on problems in commutative algebra. She intends to study the multiplicity of R/I for a homogeneous ideal I in terms of the shifts in its minimal graded resolution. She also intends to study the finite determinations of the presentations of an ideal. Finally, she intends to construct the minimal algebra resolutions for R/I where I is an ideal in the linkage class of a complete resolution. 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.