Mathematical Sciences: Von Neumann Regular Rings, Differential Operator Rings, and Noetherian Rings

这个项目涉及到非对易环理论的各个方面。主要研究者将研究von Neumann正则环、微分算子环、Notherian环和相关环的结构。对von Neumann正则环的研究也将通过Grothendieck群来研究某些偏序阿贝尔群的结构。这个项目属于环理论的一般领域。环是一种代数结构，它在代数和数学中的各种设置中实现。具体研究涉及von Neumann正则环和微分算子环的结构和理论。后一种类型的环是数学和物理的其他领域感兴趣的。

This project is concerned with various aspects of noncommutative ring theory. The principal investigator will examine the structure of von Neumann regular rings, differential operator rings, noetherian rings and related rings. The research on von Neumann regular rings will also involve, via the Grothendieck group, investigations into the structure of certain partially ordered abelian groups. This project is in the general area of ring theory. A ring is an algebraic structure which is realized in a variety of settings in algebra and mathematics. The specific research involves the structure and theory of von Neumann regular rings and rings of differential operators. The latter type of ring is of interest to other areas of mathematics and physics.