关于2可逆的置换可分环（英文）  

Separative Exchange Rings in Which 2 Is Invertible

作　　者：陈焕银[1] 

机构地区：[1]杭州师范大学数学系,杭州浙江310036

出　　处：《数学进展》2017年第4期563-569,共7页Advances in Mathematics（China）

基　　金：Supported by the Natural Science Foundation of Zhejiang Province(No.LY17A010018)

摘　　要：环R称为可分环,如果对任何有限生成投射右R-模A和B,AA≌AB≌BBA≌B.假设R是置换可分环,其中2可逆,a-a^3∈R正则,证明了a∈R单位正则当且仅当R(1-a^2)R=Rr(a)=e(a)R.环R中元素a称为特殊clean元,如果有幂等元e∈R使得a-e∈R可逆,而且aR∩eR=0.进一步,证明了a∈R是特殊clean元,如果aR/ar(a^2),R/(aR+r(a))投射,而且R(a-a^3)R=Rar(a^2)=e(a^2)aR.由此推广了正则可分环中相关结论.A ring R is separative provided that for all finitely generated projective right R-modulesA and B, A@A≌ A＋B ≌ B＋B - A ≌ B. Let Rbeaseparative exchange ring in which 2 is invertible, and let a - a3 E R be regular. In this note, we prove that a E R is unit-regular if R（1 - α2）R = Rr（α） = l（α）R. An element α in a ring R is special clean if there exists an idempotent e ∈ R such that a - e E R is a unit and aR ∩ eR =0. Furthermore, we prove that a e R is special clean if aR/ar（a2）, R/（aR ＋ r（a）） are projective and R（a-a3）R= Rar（a2） = l（a2）aR. These also extend the corresponding results in separative regular rings.

关 键 词：单位正则元 特殊clean元 可分环 置换环 

分 类 号：O153.3[理学—数学]