CoHopficity of self-injective rings (Q2739144)
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scientific article; zbMATH DE number 1643517
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | CoHopficity of self-injective rings |
scientific article; zbMATH DE number 1643517 |
Statements
24 March 2002
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co-Hopfian rings
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stable range one
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self-injective rings
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injective homomorphisms
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0.9342302
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0.9202221
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0.9177724
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0.90512264
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CoHopficity of self-injective rings (English)
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Let \(R\) be an associative ring with identity. The ring \(R\) is called co-Hopfian in Mod-\(R\) if every injective homomorphism \(f\colon R\to R\) is an isomorphism. \(R\) is said to have stable range one if for any \(a,b\in R\) satisfying \(aR+bR=R\), there exists \(y\in R\) such that \(a+by\) is a unit. The main result established by the authors is: a self-injective ring \(R\) is co-Hopfian in Mod-\(R\) if and only if \(R\) has stable range one.
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