The complete integral closure of 𝑅[𝑋]

Lucas, Thomas G.

doi:10.1090/S0002-9947-1992-1034667-4

The complete integral closure of $R[X]$
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Trans. Amer. Math. Soc. 330 (1992), 757-768 Request permission

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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