Geodesic
Exchange rings with stable range one
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 579-590.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $a,b\in R$, $R/aR\cong R/bR\Longrightarrow aR\cong bR$.
Classification : 16D70, 16E20, 16E50, 16U99, 19B10
Keywords: exchange ring; stable range one; idempotent; unit 
@article{CMJ_2007__57_2_a4,
     author = {Chen, Huanyin},
     title = {Exchange rings with stable range one},
     journal = {Czechoslovak Mathematical Journal},
     pages = {579--590},
     publisher = {mathdoc},
     volume = {57},
     number = {2},
     year = {2007},
     mrnumber = {2337616},
     zbl = {1161.16008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007__57_2_a4/}
}
TY  - JOUR
AU  - Chen, Huanyin
TI  - Exchange rings with stable range one
JO  - Czechoslovak Mathematical Journal
PY  - 2007
SP  - 579
EP  - 590
VL  - 57
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2007__57_2_a4/
LA  - en
ID  - CMJ_2007__57_2_a4
ER  - 
%0 Journal Article
%A Chen, Huanyin
%T Exchange rings with stable range one
%J Czechoslovak Mathematical Journal
%D 2007
%P 579-590
%V 57
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2007__57_2_a4/
%G en
%F CMJ_2007__57_2_a4
Chen, Huanyin. Exchange rings with stable range one. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 579-590. http://geodesic.mathdoc.fr/item/CMJ_2007__57_2_a4/