On the embedding of a commutative ring in a local ring (Q1282991)

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scientific article; zbMATH DE number 1274766
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English
On the embedding of a commutative ring in a local ring
scientific article; zbMATH DE number 1274766

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    On the embedding of a commutative ring in a local ring (English)
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    28 June 1999
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    Let \(R\) be a commutative ring with identity. The authors consider conditions in order that there exists an embedding of \(R\) in a local ring. This leads naturally to an examination of conditions in order that a quasilocal ring be dominated by a local ring. This, in turn, leads to a study of extensions of the residue field of a quasilocal ring. Several results are proved concerning domination of a quasilocal ring by a local ring including the result that a zero-dimensional quasilocal ring that is embeddable in a Noetherian ring is dominated by an Artinian local ring.
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    Noetherian ring
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    Artinian ring
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    local ring
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    quasilocal ring
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    embedding in a local ring
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    extension
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