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Displaying similar documents to “Stable rings generated by their units.”

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 .