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

点击翻译按钮获取中文摘要

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.