Mathematical Sciences: Crossed Products over Rational Function Fields

这个项目涉及到司的结构 环，中心单代数，以及它们联合收割机的方式 形成布劳尔团体。 使用有限群，可以 将除法环描述为叉积。 最终目标是 把群的结构和算术性质联系起来 戒指的中心。 支持的研究是在环的一般领域 理论 一个环是一个代数对象有一个加法和一个 乘法定义在它上面。环自然地出现在许多领域 数学。 这位首席研究员将研究 戒指可以容纳另一个。 这项工作借鉴了一些深层次的结果， 群论，并将阐明各种问题，代数 和数论

This project is concerned with the structure of division rings, central simple algebras, and the ways in which they combine to form Brauer groups. Using finite groups, it is possible to describe division rings as crossed products. An ultimate goal is to relate the structure of the group with the arithmetic properties of the center of the ring. The research supported is in the general area of ring theory. A ring is an algebraic object having an addition and a multiplication defined on it. Rings occur naturally in many areas of mathematics. This principal investigator will study how one ring can contain another. The work draws on some deep results in group theory and will shed light on various questions in algebra and number theory.