Displaying similar documents to “Exchange rings with stable range one”

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.

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 .

Strong separativity over exchange rings

Huanyin Chen (2008)

Czechoslovak Mathematical Journal

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An exchange ring R is strongly separative provided that for all finitely generated projective right R -modules A and B , A ⊕ A ≅ A ⊕ B ⇒ A ≅ B . We prove that an exchange ring R is strongly separative if and only if for any corner S of R , a S + b S = S implies that there exist u , v ∈ S such that a u = b v and S u + S v = S if and only if for any corner S of R , a S + b S = S implies that there exists a right invertible matrix a b * ∈ M 2 ( S ) . The dual assertions are also proved.