Mathematical Sciences: Structure of Rings and Modules

本研究的目的是研究诺特环， 仿射代数及其表示 理论主要研究者将研究 模与应用程序的局部化Noether环。 注意力将集中在一个诺特的链接图 环，以及该图中包含的信息如何预测 一个模块的可能扩展。有限环的理想理论 扩展也将被考虑，希望利用最近的 在这一领域取得进展，以取得成果， 环和有限扩张环的理论是相关的。的 首席研究员还将研究仿射代数的 多项式有界增长，特别是关于Gelfand- Kirillov维数和相应的Poincare级数。在整个 将重点建设和研究 适当的例子。 环是既有加法又有加法的代数对象 乘法这些物体自然出现在许多领域， 数学给定一个环，一个重要的方面是如果一个环 包含原始的一个存在具有某些属性。的 何时可以本地化的问题就是这种类型， 是环论的中心话题

The aim of this research is to study Noetherian rings and affine algebras, with special reference to their representation theory. The principal investigator will study extensions of modules with applications to localizations of Noetherian rings. Attention will be focused on the graph of links of a Noetherian ring, and how information contained in this graph can predict the possible extensions of a module. The ideal theory of finite ring extensions will also be considered in the hopes of using recent progress in this area to obtain results on how the representation theories of a ring and a finite extension ring are related. The principal investigator will also study affine algebras of polynomial bounded growth, with special reference to the Gelfand- Kirillov dimension and the associated Poincare series. Throughout there will be an emphasis on the construction and study of appropriate examples. A ring is an algebraic object having both an addition and a multiplication. These objects arise naturally in many areas of mathematics. Given a ring, one area of importance is if a ring containing the original one exists having certain properties. The question of when it is possible to localize is of this type and is a central topic in ring theory.