Displaying similar documents to “Exchange rings having stable range one.”

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 ∈ 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 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.

Diagonal reductions of matrices over exchange ideals

Huanyin Chen (2006)

Czechoslovak Mathematical Journal

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In this paper, we introduce related comparability for exchange ideals. Let I be an exchange ideal of a ring R . If I satisfies related comparability, then for any regular matrix A ∈ M n ( I ) , there exist left invertible U 1 , U 2 ∈ M n ( R ) and right invertible V 1 , V 2 ∈ M n ( R ) such that U 1 V 1 A U 2 V 2 = diag ( e 1 , ⋯ , e n ) for idempotents e 1 , ⋯ , e n ∈ I .