Rings with many idempotents.

Chen, Huanyin

Displaying similar documents to “Rings with many idempotents.”

Exchange rings having stable range one.

Chen, Huanyin (2001)

International Journal of Mathematics and Mathematical Sciences

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Exchange rings satisfying the related comparability.

Huanyin Chen, Fu-An Li (2002)

Collectanea Mathematica

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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.

Whitehead groups of exchange rings with primitive factors Artinian.

Chen, Huanyin, Li, Fu-an (2001)

International Journal of Mathematics and Mathematical Sciences

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Near-rings with a special condition on idempotents.

Heatherly, H.E., Courville, J.R. (1999)

Mathematica Pannonica

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Exchange rings with stable range one

Huanyin Chen (2007)

Czechoslovak Mathematical Journal

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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 $a R \cap e R = 0$ if and only if for any regular $a \in R$ , there exist $e \in r . a n n (a^{+})$ and $u \in U (R)$ such that $a = e + u$ if and only if for any $a, b \in R$ , $R / a R ≅ R / b R ⟹ a R ≅ b R$ .

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

Huanyin Chen (2008)

Czechoslovak Mathematical Journal

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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.