Mathematical Sciences: Non-Commutative Ring Theory

该项目涉及以下各个领域： 非交换环理论 主要研究者将 研究PI环及其表示，着重于应用 线性组，规范化元素的行为和 PI环在矩阵中的可嵌入性 仿射素环 Gelfand-Kirillov维度2也将被研究， 目的是确定它们何时是原始的。 最后， 一类非交换代数上约化群不变量 将被考虑。 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 project is concerned with various areas of noncommutative ring theory. The principal investigator will study PI rings and their representations focusing on applications to linear groups, the behavior of normalizing elements and the embeddability of PI rings into matrices. Affine prime rings with Gelfand-Kirillov dimension two will also be investigated with the goal of determining when they are primitive. Finally, rings of invariants of reductive groups on certain noncommutative algebras will be considered. 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.