Mathematical Sciences: Regular Graded Noetherian Rings

这个奖项是关于非交换的理论 Noether环，特别是连通分次的Noether环 满足Artin-Schelter（AS）正则性条件的代数。 AS正则环一直是一个相当多的研究课题 最近，因为它们提供了真正新的几何技术， 为研究非交换环，并与其他 当前感兴趣的领域，特别是量子群。 校长 研究人员将研究其中具体而重要的例子， 代数发展AS正则代数的抽象理论 以及"非交换射影几何"的相关理论。 首席研究员还将致力于扩大现有的 有限整体连通分次Noether PI环的一些结果 维度 这项研究是在环理论的一般领域。 的环 是一个既有加法又有 乘法定义。虽然加法运算 满足交换律，乘法运算是 不需要这样做。 一个环的例子， 乘法不是交换的是nxn的集合 整数上的矩阵。 非交换环的研究 已经成为代数的一个重要组成部分，因为它的增长 对数学和物理学的其他分支具有重要意义。

This award is concerned with the theory of noncommutative Noetherian rings, particularly with that of connected graded algebras satisfying the Artin-Schelter (AS) regularity condition. The AS regular rings have been a subject of considerable research recently, since they provide genuinely new, geometric techniques for the study of noncommutative rings and are related to other areas of current interest, notably quantum groups. The principal investigator will study specific, important examples of these algebras to develop the abstract theory of AS regular algebras and the related theory of "noncommutative projective geometry". The principal investigator will also work on extending existing results on connected graded, Noetherian PI rings of finite global dimension. This research is in the general area of ring theory. A ring is an algebraic object having both an addition and a multiplication defined on it. Although the additive operation satisfies the commutative law, the multiplicative operation is not required to do so. An example of a ring for which multiplication is not commutative is the collection of nxn matrices over the integers. The study of noncommutative rings has become an important part of algebra because of its increasing significance to other branches of mathematics and physics.