【作者】 姜秀萍；

【导师】 侯成军；

【作者基本信息】 曲阜师范大学 ， 基础数学， 2007， 硕士

【摘要】 全文分为三章。第一章证明了多项式代数C[x]到多项式代数自由积C[x]*C[y]内的每个局部1-上循环是1-上循环，即C[x]到C[x]*C[y]内的局部导子是导子。第二章研究了由幂等元生成的Banach代数上的局部上循环问题。在一定条件下，证明了此代数到其Banach双模上的有界局部2-上循环仍是2-上循环。第三章引入Banach代数的逼近局部上循环的概念，证明了von Neumann代数到其正规对偶双模上的每个逼近局部2-和3-上循环，都是2-和3-上循环。更多还原

【Abstract】 The thesis consists of three chapters.In chapter 1, we prove that every local 1-cocycle from polynomial algebra C[x] into noncommutative polynomial algebra C[x]*C[y] is a 1-cocycle; In other words, every local derivation from C[x] into C[x]*C[y] is a derivation.In chapter 2, we study the local cocycle of a special kind of Banach algebra, generated linearly by its idempotents, under some conditions, we show that every local 2-cocycle of such a Banach algebra is still a 2-cocycle.In chapter 3, we introduce the notion of approximative local cocycle from Banach algebras into their Banach bimodules, and show that every approximative local k-cocycle of von Neumann algebra into itself is a k-cocycle,for k=2,3.更多还原