半素环扩张中心上的模(英文)  

Modules Over Extended Centroids of Semiprime Rings

作　　者：魏峰[1] 张淑华[1] 牛凤文[1] 

机构地区：[1]吉林大学数学研究所

出　　处：《数学进展》2002年第3期257-260,共4页Advances in Mathematics（China）

基　　金：The work is supported by the Doctoral Fundation of the Educational Committee of China.

摘　　要：设C为半素环R的扩张中心.通过C中的幂等元,我们可以在任意C-模上建立拓扑空间.从拓扑学角度出发,我们证明:殆Hausdorff C-模为内射模.此外,我们给出殆Hausdorff C-模的一种有趣刻画:若M和N都是殆Hausdorff C-模,则存在一个幂等元e∈C,使得Me可嵌入到Ne中且N(1-e)可嵌入到M(1-e)中.Let C be the extended centroid of a semiprime ring R. We can establish topological space on any C-module through the idempotents of C. From the point of view of topology, we will prove that any complete almost Hausdorff C-module is injective. Moreover, one kind of characterizations concerning complete almost Hausdorff C-modules is given. That is, if M and N are complete almost Hausdorff C-modules, then there exists an idempotent element e in C such that Me embeds in Ne and N(1-e) embeds in M(1-e).

关 键 词：半素环 扩张中心 完备模 殆Hausdorff C-模 内射模 

分 类 号：O153.3[理学—数学]