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The ideal transform and overrings of an integral domain

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References

  1. 1.

    Gilmer, R. W., Jr.: A class of domains in which primary ideals are valuation ideals. Math. Ann.161, 247–254 (1965).

  2. 2.

    —, and W. J. Heinzer: Overrings of Prüfer domains. II. J. Algebra7, 281–301 (1967).

  3. 3.

    ——: Intersections of quotient rings of an integral domain. J. Math. Kyoto Univ.7, 133–150 (1967).

  4. 4.

    Gilmer, R. W., Jr., and W. J. Heinzer: On the number of generators of an invertible ideal. (Submitted for publication).

  5. 5.

    Nagata, M.: On the derived normal rings of Noetherian integral domains. Mem. Coll. Sci. Kyoto Univ.29, 293–303 (1955).

  6. 6.

    —: A treatise on the 14th problem of Hilbert. Mem. Coll. Sci. Kyoto Univ.30, 57–82 (1956).

  7. 7.

    Nagata, M.: Some sufficient conditions for the fourteenth problem of Hilbert. Actas Del Coloquio Internac. Sobre Geometria Algebraica, p. 107–121, 1965.

  8. 8.

    —: Local rings. New York: Interscience 1962.

  9. 9.

    Ohm, J.: Integral closure and (x,y)n=(xn,yn). Monatsh. für. Math.71, 32–39 (1967).

  10. 10.

    Zariski, O., and P. Samuel. Commutative algebra, vol. I. Princeton, New Jersey: Van Nostrand 1958.

  11. 11.

    ——. Commutative algebra, vol. II. Princeton, New Jersey: Van Nostrand 1960.

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Brewer, J. The ideal transform and overrings of an integral domain. Math Z 107, 301–306 (1968). https://doi.org/10.1007/BF01110018

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Keywords

  • Integral Domain