Abstract:
Among the several types of closures of an ideal I that have been defined and studied in the past decades, the integral closure has a central place being one of the earliest and most relevant. Despite this role, it is often a difficult challenge to describe it concretely once the generators of I are known. Our aim in this note is to show that in a broad class of ideals their radicals play a fundamental role in testing for integral closedness, and in case , is still helpful in finding some fresh new elements in . Among the classes of ideals under consideration are: complete intersection ideals of codimension two, generic complete intersection ideals, and generically Gorenstein ideals.
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Received: 28 July 1997
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Corso, A., Huneke, C. & Vasconcelos, W. On the integral closure of ideals. manuscripta math. 95, 331–347 (1998). https://doi.org/10.1007/s002290050033
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DOI: https://doi.org/10.1007/s002290050033