The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Rings with many idempotents.”

Exchange rings satisfying the related comparability.

Huanyin Chen, Fu-An Li (2002)

Collectanea Mathematica

Similarity:

In this paper we investigate the related comparability over exchange rings. It is shown that an exchange ring R satisfies the related comparability if and only if for any regular x C R, there exists a related unit w C R and a group G in R such that wx C G.

Exchange rings with stable range one

Huanyin Chen (2007)

Czechoslovak Mathematical Journal

Similarity:

We characterize exchange rings having stable range one. An exchange ring R has stable range one if and only if for any regular a R , there exist an e E ( R ) and a u U ( R ) such that a = e + u and a R e R = 0 if and only if for any regular a R , there exist e r . a n n ( a + ) and u U ( R ) such that a = e + u if and only if for any a , b R , R / a R R / b R a R b R .

Exchange rings in which all regular elements are one-sided unit-regular

Huanyin Chen (2008)

Czechoslovak Mathematical Journal

Similarity:

Let R be an exchange ring in which all regular elements are one-sided unit-regular. Then every regular element in R is the sum of an idempotent and a one-sided unit. Furthermore, we extend this result to exchange rings satisfying related comparability.