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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The complete integral closure of $ R[X]$


Author: Thomas G. Lucas
Journal: Trans. Amer. Math. Soc. 330 (1992), 757-768
MSC: Primary 13B22
DOI: https://doi.org/10.1090/S0002-9947-1992-1034667-4
MathSciNet review: 1034667
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Abstract: For a reduced ring $ R$ that is completely integrally closed it is not always the case that the corresponding polynomial ring $ R[X]$ is completely integrally closed. In this paper the question of when $ R[X]$ is completely integrally closed is shown to be related to the question of when $ R$ is completely integrally closed in $ T(R[X])$ the total quotient ring of $ R[X]$. A characterization of the complete integral closure of $ R[X]$ is given in the main theorem and this result is used to characterize the complete integral closure of the semigroup ring $ R[S]$ when $ S$ is a torsion-free cancellative monoid.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1034667-4
Keywords: Almost integral, complete integral closure, complete ring of quotients, dense ideal
Article copyright: © Copyright 1992 American Mathematical Society