Journal of Science of the Hiroshima University, Series A-I (Mathematics)

On overrings of a domain

H. S. Butts and Nick Vaughan

Full-text: Open access

Article information

Source
J. Sci. Hiroshima Univ. Ser. A-I Math., Volume 33, Number 1 (1969), 95-104.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206138590

Digital Object Identifier
doi:10.32917/hmj/1206138590

Mathematical Reviews number (MathSciNet)
MR0245564

Zentralblatt MATH identifier
0177.06403

Subjects
Primary: 13.15

Citation

Butts, H. S.; Vaughan, Nick. On overrings of a domain. J. Sci. Hiroshima Univ. Ser. A-I Math. 33 (1969), no. 1, 95--104. doi:10.32917/hmj/1206138590. https://projecteuclid.org/euclid.hmj/1206138590


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References

  • [1] Bourbaki, N., Elements de Mathematique, Algebra Commutative, (a) Chapters 5 and 6, 1964, (b) Chapter 7, 1965.
  • [2] Butts, H. S. and Cranford, R. H., Some Containment Relations between Classes of Ideals in an Integral Domain, J. Sci. Hiroshima Univ. Ser. A-I 29 (1965), 1-10.
  • [3] Butts, H. S. and Phillips, R. C, Almost Multiplication Rings, Canad. J. Math., 17 (1965), 267-277.
  • [4] Butts, H. S. and Smith, W. W., On the Integral Closure of a Domain, Jour, of Sci. Hiroshima Univ. Ser. Al, vol. 30, No. 2, 1966. >
  • [5] Butts, H. S. and Smith, W. W., Prfer Rings, Math. Zeitschr 95, 196-211, 1967.
  • [6] Cohen, I. S., Commutative Rings with Restricted Minimum Condition, Duke Math. J., 17 (1950), 27- 42.
  • [7] Cranford, R. H., Relations between Classes of Ideals in an Integral Domain (Louisiana State University Library, Doctoral Dissertation, 1964).
  • [8] Gilmer, R. W., Overrings of Prfer Domains, Journal of Algebra, Vol. 4, No. 3 (1966), 331-340.
  • [9] Gilmer, R. W., Integral Domains which are almost Dedekind, Proc. Amer. Math. Soc. 15 (1964), 813-818.
  • [10] Gilmer, R. W. and Ohm, J., Primary Ideals and Valuation Ideals, Trans. Amer. Math. Soc, 117 (1965), 237-250.
  • [11] Gilmer, R. W. and Ohm, J., Integral Domains with Quotient Overrings, Math. Annalen, 153 (1964), 97-103.
  • [12] Krull, W., Ideatheorie, Chelsea (1948).
  • [13] Krull, W., Beitrage zur Arithmetik Kommutativer Integritateberiche, Math. Zeit., 41 (1936), 545-569.
  • [14] Krull, W., Algemeine Bewertungstheorie, J. Reine Angew. Math., 167 (1931), 160-196.
  • [15] Mann, H. B., Introduction to Algebraic Number Theory, The Ohio State Press, Columbus, 1955.
  • [16] Nagata, M., Local Rings, Interscience (1962).
  • [17] Nakano, N., Uber die Umkehrbarkeit der Ideals im Integritatsbereiche, Proc. Imp. Acad. Tokyo, 19 (1943), 230-234.
  • [18] Ohm, J., Some Counterexamples Related to Integral Closure in /)[[*]], Trans. Amer. Math. Soc, vol. 122, No. 2, 321-333, 1966.
  • [19] Samuel, P., Lectures on Unique Factorization Domains, Tata Institute of Fundamental Research, Bombay, 1964.
  • [20] Tramel, S., Factorizations of Principal Ideals in the Sense of Quasi-equality, submitted for publication.
  • [21] Zariski, O., and Samuel, P., Commutative Algebra, Vol. 1, van Nostrand (1958).
  • [22] Zariski, O. and Samuel, P., Commutative Algebra, Vol. 2, van Nostrand (1961).