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

Some containment relations between classes of ideals in an integral domain

H. S. Butts and R. H. Cranford

Full-text: Open access

Article information

Source
J. Sci. Hiroshima Univ. Ser. A-I Math., Volume 29, Number 1 (1965), 1-10.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206139308

Digital Object Identifier
doi:10.32917/hmj/1206139308

Mathematical Reviews number (MathSciNet)
MR0184958

Zentralblatt MATH identifier
0136.31601

Subjects
Primary: 13.15
Secondary: 16.00

Citation

Butts, H. S.; Cranford, R. H. Some containment relations between classes of ideals in an integral domain. J. Sci. Hiroshima Univ. Ser. A-I Math. 29 (1965), no. 1, 1--10. doi:10.32917/hmj/1206139308. https://projecteuclid.org/euclid.hmj/1206139308


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References

  • [1] R. Gilmer and J. Ohm, "Primary Ideals and Valuation Ideals", to appear in Trans, of Amer. Math. Soc.
  • [2] R. Gilmer, "Some Containment Relations between Classes of Ideals in a Commutative Ring", to appear in Proc. Am. Math Soc.
  • [3] R. Gilmer, Integral Domains which are almost Dedekind", to appear in Proc. Am. Math. Soc.
  • [4] R. Gilmer, "The Cancellation Law for Ideals in a Commutative Ring", to appear in Canadian Jour, of Math.
  • [5] R. Gilmer, "Rings in which Semi-Primary Ideals are Primary", Pac. Jour, of Math., vol. 12, No. 4, 1962, pp. 1273-1276.
  • [6] R. Gilmer, "Extension of Results Concerning Rings in which every Semi-primary Ideal is Primary", to appear in Duke Math. Jour.
  • [7] H. Butts and C. Phillips, "Almost Multiplication Rings", to appear in Canadian Jour, of Math.
  • [8] H. Butts and R. Gilmer, "Primary Ideals and Prime Power Ideals", submitted to Tran. Am. Math. Soc.
  • [9] O. Zariski and P. Samuel, "Commutative Algebra", vol. 1, van Nostrand (1958).
  • [10] O. Zariski and P. Samuel, "Commutative Algebra", vol. 2, van Nostrand, (1961).
  • [11] W. Krull, "Beitrage zur Arithmetik Kommutativer Integrittsberiche", Math. Zeit. 41 (1936), pp. 545- 569.
  • [12] W. Krull, "Ideal theoe", Chelsea (1948).
  • [13] H. Prufer, "Untersuchungen ber Teilbarkeitseigenshaften in Korpern", J. Reine Angew. Math. 168 (1932), 1-36.
  • [14] M. Nagata, "Local Rings", Intersciene (1962).
  • [15] I. S. Cohen, "Commutative Rings with Restricted Minimum Condition", Duke Math. Journal 17 (1950), pp. 27-42.