Problems in Noetherian Rings

9700682阿伯巴赫该奖项支持在交换代数中的几个问题上的工作。其中包括研究Huneke关于参数理想的关系型猜想，参数检验理想的局部化，以及一般紧闭包的局部化。这项研究涉及到交换代数和代数几何中的一些问题。代数几何研究多项式方程族的解。人们既可以研究解集的几何，也可以通过研究解集上的某些函数来代数地处理问题，这些函数构成了所谓的交换环。这种双重视角在交换代数和代数几何之间建立了紧密的联系。

9700682 Aberbach This award supports work on several problems in commutative algebra. These include studying Huneke's relation-type conjecture for parameter ideals, localization of parameter test ideals, and localization of tight closure in general. This research is concerned with a number of questions in commutative algebra and algebraic geometry. Algebraic geometry studies solutions of families of polynomial equations. One can either study the geometry of the solution set or approach problems algebraically by investigating certain functions on the solution set that form what is called a commutative ring. This dual perspective creates a close connection between commutative algebra and algebraic geometry.