拓扑空间和近Clean环  

Topological Spaces and Nearly Clean 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：《数学年刊（A辑）》2010年第3期321-330,共10页Chinese Annals of Mathematics

基　　金：浙江省自然科学基金(No.Y6090404);杭州师范大学基金(No.200901)资助的项目

摘　　要：元a∈R称为近clean的,如果它是幂等元和满元素的和.若环R中的每一个元都是近clean元,则环R称为近clean环.在此定义下,证明了对Abel环R,下列结论是等价的:(1)R是近clean的;(2)■a∈R,■e=e^2∈R,使得V(a)■V(e)且V(1-a)■V(1-e);(3)适中空间Ξ(R)是强零维的;(4)R是pm环且Max(R)是强零维的.某些近clean元的判别也可由此得到.An element a∈R is nearly clean if it is the sum of an idempotent and a full element.A ring R is nearly clean if every element in R is nearly clean.The author proves that for an Abelian ring R,the following are equivalent：（1）R is nearly clean;（2）For any a∈R,there exists an idempotent e∈R such that V（a）■V（e）and V（1-a）■V（1-e）; （3）The medium spaceΞ（R）is strongly zero-dimensional;（4）R is a pm ring and Max（R）is strongly zero-dimensional.The criteria for some nearly clean elements are also obtained.

关 键 词：近clean环 强零维环 适中空间 

分 类 号：O153.3[理学—数学]