Gorenstein rings as specializations of unique factorization domains (Q788059)

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scientific article; zbMATH DE number 3842030
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Gorenstein rings as specializations of unique factorization domains
scientific article; zbMATH DE number 3842030

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    Gorenstein rings as specializations of unique factorization domains (English)
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    1984
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    Let R be a Gorenstein ring which is a factor ring of a regular local ring and a complete intersection locally in codimension one. The major result proves that R is a specialization of a unique factorization domain (UFD) that is Cohen-Macaulay and an epimorphic image of a regular local ring. This result is used to show that for certain singularities the highest exterior power and any symmetric power of the module of differentials are never Cohen-Macaulay. Examples are constructed of a local Cohen-Macaulay UFD S whose singular locus has large codimension, but the completion of S is not a UFD.
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    Gorenstein ring
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    Cohen-Macaulay ring
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    unique factorization ring
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    UFD
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    regular local ring
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    module of differentials
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    singular locus
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    completion
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