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 .

Stable elements of Banach and Fréchet algebras

Graham Allan (1998)

Studia Mathematica

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We introduce an algebraic notion-stability-for an element of a commutative ring. It is shown that the stable elements of Banach algebras, and of Fréchet algebras, may be simply described. Part of the theory of power-series embeddings, given in [1] and [4], is seen to be of a purely algebraic nature. This approach leads to other natural questions.