具有拟稳定秩的环  

Rings with Quasi-Stable Range Conditions

作　　者：孙晓青[1] 田径[1] 李江华[1] 

机构地区：[1]西安理工大学理学院,陕西西安710054

出　　处：《西安理工大学学报》2013年第2期188-191,共4页Journal of Xi'an University of Technology

基　　金：陕西省自然科学基金资助项目(2012K06-43);陕西省教育厅专项计划基金资助项目(12JK0874);西安理工大学博士启动基金(108-211105)

摘　　要：为了将拟可逆元引入到稳定秩条件中,提出了具有拟稳定秩的环。利用具有拟稳定秩的环的特殊性质,证明了环R是具有拟稳定秩的环的充分必要条件是对任意满足条ax+b=1件的a,b∈R,存在w∈Rq-1使得a+bw∈U(R),以及其他等价条件,体现了具有拟稳定秩的环良好的结构特点。To purpose is to conceptually weave quasi-invertibility into the stable range condition, this pa- per proposed the concept of the ring with quasi-stable range condition. The special properties of the ring with quasi-stable range condition are used to prove that R is the ring with quasi-stable range condition if and only if for any a,b ∈R satisfying ax ＋ b = 1, there exists w ∈Rq-; such that a ＋ bw ∈ U（R）, and other conditions of equivalence. The study reflected that the ring with quasi-stable range condition have well structures.

关 键 词：可逆元 拟可逆元 具有稳定秩条件的环 

分 类 号：O153.3[理学—数学]