Weyl型代数的环论性质(英文)  

Ring Theoretical Properties of Weyl Type Algebras

作　　者：王志玺[1] 李星梅[1] 

机构地区：[1]首都师范大学数学系,北京100037

出　　处：《数学进展》2004年第5期570-574,共5页Advances in Mathematics（China）

基　　金：Supported by the NSFC(No. 10271081) and the NSF of Beijing.

摘　　要：设A是代数闭域κ上有单位元1的交换结合代数, D是A的交换κ-导子组成的非零κ-向量空间.苏育才与赵开明引进Weyl型代数A[D]并且证明了结合代数A[D]是单代数当且仅当A是D-单的且κ1[D]在A上的作用为忠实的.通过证明A[D]与smaLsh productA＃U(D)同构,我们给出了这一结果的一个纯环论的证明,同时给出了A[D]的一个Ore扩张实现.Let A be a commutative associative algebra with an identity 1 over an algebraically closed field k and D a nonzero fc-vector space of commuting κ-derivations of A. Su Yucai and Zhao Kaiming introduced the Weyl type algebra A[D] and proved that A[D], as an associative algebra, is simple if and only if A is D-simple and κ1 [D] acts faithfully on A. We give a pure ring theoretical proof for this result by proving there is an isomorphism between A[D] and the smash product A#U(D). Then we give an Ore extension realization of A[D].

关 键 词：环论 证明 单位元 交换结合代数 导子 ORE扩张 同构 引进 育才 作用 

分 类 号：O153.3[理学—数学] O152.5[理学—基础数学]