Mathematical Sciences: Division Algebras, Brauer Groups, andField Theory

本计画是关于除代数的研究， 布劳尔群和场论。有两个部分， research.首先是研究当地的布劳尔团体， 第二个是要表达一个 一类在Brauer群作为产品的循环代数在一个 明确的方式。 支持的研究是在一般领域的领域 理论域是类似于有理数的代数结构 数字、真实的数字和复数， 一个非零元素有一个关于乘法的逆。 场论是一门丰富而深刻的学科， 根源来自早期试图系统地 描述多项式的零点。

This project concerns research on division algebras, Brauer groups, and field theory. There are two parts to the research. The first is to study local Brauer groups in dimensions greater than two, and the second is to express a class in the Brauer group as a product of cyclic algebras in an explicit way. The research supported is in the general area of field theory. Fields are algebraic structures similar to the rational numbers, the real numbers, and the complex numbers in that each nonzero element has an inverse with respect to multiplication. Field theory is a rich and deep subject with its historical roots arising from the early attempts to systematically describe the zeros of polynomials.