Mathematical Sciences: The Invariants of n x n Matrices

所支持的项目涉及域K上r个一般n×n矩阵的不变量环C(n，r)和迹环R(n，r)。主要问题是找到C(n，r)作为K上的代数和R(n，r)作为C(n，r)上的代数的表示。该项目还将考虑生成集中元素的最小次数以及C(n，r)的商域是否在K上纯超越。支持的研究涉及矩阵理论、环理论和不变量的计算。特别是，这涉及到一个老问题，即确定在各种变换下保留哪些数学函数。这在许多科学领域和数学领域都很有趣。

The project supported concerns the ring of invariants, C(n,r), of a set of r generic nxn matrices over a field K and the trace ring, R(n,r). The main problem is to find presentations for C(n,r) as an algebra over K and R(n,r) as an algebra over C(n,r). The project will also consider the minimal degree of elements in a generating set and whether the quotient field of C(n,r) is purely transcendental over K. The research supported concerns matrix theory, ring theory and the calculation of invariants. In particular, this involves an old problem of determining what mathematical functions are preserved under various transformations. This is of interest in many areas of science as well as in mathematics.