Mathematical Sciences: Research in Commutative Algebra

这个建议支持了H. Srinivasan教授对交换代数问题的研究。她打算从最小梯度分辨率的变化来研究齐次理想I的R/I的多重性。她还打算研究理想表象的有限决定。最后，她打算构造R/I的最小代数分辨率，其中I是完全分辨率的连杆类中的理想。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。

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.