摘要介绍了“代数”这种代数结构,即域上的代数是指域上的向量空间,在上定义了满足双线性的一种乘法运算,使关于乘法和自身加法构成一个环。证明了一个紧拓扑空间上的所有连续函数对一般函数的加法、乘法和数乘运算构成一个代数。定义了前述代数上的一个范数,讨论了这个赋范线性空间的性质,并推广了数学分析中一致连续函数列的连续性定理。通过构造,考虑了紧拓扑空间上的闭集与前述代数作为一个环所拥有的闭理想,证明了它们之间具有一一对应的关系。最后考虑了以连续函数作为矩阵的元素所形成的矩阵代数,证明了它的理想和前述代数的理想一一对应。83945

毕业论文关键词  代数  环  闭集  连续  理想

毕业设计说明书外文摘要

Title  Self-adjoint Matrix Algebras And Its Applications

Abstract In this paper,we introduce an algebraic structure called "algebras"。An algebras is a linear space A on a field F and there’s an operation called "multiplication" on A satisfying F-bilinear,making A a ring。We provide the proof that all continuous functions on a compact topological space constitute an algebras。We define a norm on the former algebras and generalize the theorem of uniform continuity to that normed space。By construction,we proof that there exists a bijection between all closed sets of that compact topological space and all ideals of the normed space。At last,we proof that there exists a one-to-one correspondence between ideals of the matrix algebras and the ideals of the former algebras。

Keywords  algebras; ring; closed set; continuity; ideal

目   次

1   绪论………………………………………………………………………………………… 1

1。1 国内外发展综述 ……………………………………………………………………… 1

1。2 课题内容综述 …………………………………………………………………………… 1

2 预备知识 …………………………………………………………………………… 2

3 主要结论 …………………………………………………………………………… 4

3。1 上连续函数所形成的代数…………………………………………………………… 4

3。2 的闭理想…………………………………………………………………………… 8

3。3 的理想……………………………………………………………………… 10