1. Exchange rings with stable range one
- Creator:
- Chen, Huanyin
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- exchange ring, stable range one, idempotent, and unit
- Language:
- English
- Description:
- We characterize exchange rings having stable range one. An exchange ring $R$ has stable range one if and only if for any regular $a\in R$, there exist an $e\in E(R)$ and a $u\in U(R)$ such that $a=e+u$ and $aR\cap eR=0$ if and only if for any regular $a\in R$, there exist $e\in r.ann(a^+)$ and $u\in U(R)$ such that $a=e+u$ if and only if for any $a,b\in R$, $R/aR\cong R/bR\Longrightarrow aR\cong bR$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public