关于置换环上强可分性的注记  

A Note on Strongly Separativity over Exchange Rings

作　　者：陈焕艮[1] 

机构地区：[1]杭州师范大学数学系,杭州310036

出　　处：《数学物理学报（A辑）》2009年第2期378-382,共5页Acta Mathematica Scientia

基　　金：杭州师范大学科研启动经费资助

摘　　要：环R是强可分的,如果对任意有限生成投射R-模A,B,A⊕A≌B⊕B,则A≌B.该文证明了置换环上的强可分性在亚直积下是不变量.作为应用,证明了R/(IJ)是强可分的当且仅当R/(I∩J)是强可分的.A ring R is strongly separative provided that, for any finitely generated projective right R-modules A and B, A ＋ A ≌ A ＋ B → A ≌ B. The author proves, in this note, that strongly separativity over exchange rings is invariant under subdirect products. As an application, the author proves that R/ （I J） is strongly separative if and only if so does R/ （I ∩ J） for any ideals of an exchange ring.

关 键 词：置换环 强可分性 直积. 

分 类 号：O153.3[理学—数学]