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Integrally closed pairs

Part of the Lecture Notes in Mathematics book series (LNM,volume 311)

Abstract

In the discussion following Gilmer's address Kaplansky introduced the notion "integrally closed pair", raised the question of characterizing these pairs and conjectured an approximate answer. Mott wisely conjectured that the methods of Davis' thesis [1] might well provide an answer. This note establishes the validity of both conjectures, at least in the Noetherian case, and somewhat more generally, for Krull domains.

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References

  1. Davis, E. D. Overrings of commutative rings. II. Integrally closed overrings, Trans. A.M.S. 110 (1964) 196–212.

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  2. Gilmer, R. W. Multiplicative Ideal Theory, Queen's Papers on Pure and Applied Mathematics-No. 12, Queen's University, Kingston, Ontario (1968).

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  3. Krull, W. Einbettungsfreie, fast-Noethersche Ringe und ihre Oberringe, Math. Nachr. 21 (1960) 319–338.

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© 1973 Springer-Verlag

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Davis, E.D. (1973). Integrally closed pairs. In: Brewer, J.W., Rutter, E.A. (eds) Conference on Commutative Algebra. Lecture Notes in Mathematics, vol 311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068923

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  • DOI: https://doi.org/10.1007/BFb0068923

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06140-3

  • Online ISBN: 978-3-540-38340-6

  • eBook Packages: Springer Book Archive