The complete integral closure of

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 | References | Similar Articles | Additional Information

Abstract: For a reduced ring that is completely integrally closed it is not always the case that the corresponding polynomial ring is completely integrally closed. In this paper the question of when is completely integrally closed is shown to be related to the question of when is completely integrally closed in the total quotient ring of . A characterization of the complete integral closure of is given in the main theorem and this result is used to characterize the complete integral closure of the semigroup ring when is a torsion-free cancellative monoid.

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Additional Information

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