Mathematical Sciences: Homological Dimensions in Noncommutative Rings

这个项目是关于有限整体维度的环，特别是交换离散赋值环上的经典序以及相关的有限整体维度的Artin环。主要的研究人员将考虑获得具有有限整体维度的Notherian PI环的整体维度的上界的问题。还将研究有限整体维序和Artin代数的结构。这将有助于破解塔西的猜想。这个项目属于环理论的一般领域。它涉及到一类环的整体维度。GOBAL尺寸测量环的某些属性。这项研究将试图确定对于一类受限的环，这一测量是否存在上限。

This project is concerned with rings of finite global dimension, particularly classical orders over a commutative discrete valuation ring and related Artinian rings of finite global dimension. The principal investigator will consider the problem of obtaining an upper bound on the global dimension of Noetherian PI rings which have finite global dimension. The structure of orders and Artin algebras of finite global dimension will also be studied. This will be useful in attacking Tarsy's conjecture. This project is in the general area of ring theory. It is concerned with the global dimension of a class of rings. The gobal dimension measures certain properties of a ring. This research will try to determine if there is an upper bound on this measurement for a restricted class of rings.