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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Rings in which the unique primary decomposition theorem holds


Author: Robert W. Gilmer
Journal: Proc. Amer. Math. Soc. 14 (1963), 777-781
MSC: Primary 13.15
MathSciNet review: 0153693
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  • [1] Keizo Asano, Über kommutative Ringe, in denen jedes Ideal als Produkt von Primidealen darstellbar ist, J. Math. Soc. Japan 3 (1951), 82–90 (German). MR 0043769
  • [2] I. S. Cohen, Commutative rings with restricted minimum condition, Duke Math. J. 17 (1950), 27–42. MR 0033276
  • [3] Shinziro Mori, Ueber eindeutige Reduktion von Idealen in Ringen ohne Teilerkettensatz, Hiroshima J. cei. 3 (1933), 275-318.
  • [4] Noboru Nakano, Über die Umkehrbarkeit der Ideale im Integritätsbereiche, Proc. Imp. Acad. Tokyo 19 (1943), 230–234 (German). MR 0014071
  • [5] B. L. van der Waerden, Modern algebra, Vol. II, 2nd ed., Ungar, New York, 1950.
  • [6] Oscar Zariski and Pierre Samuel, Commutative algebra, Volume I, The University Series in Higher Mathematics, D. Van Nostrand Company, Inc., Princeton, New Jersey, 1958. With the cooperation of I. S. Cohen. MR 0090581

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DOI: https://doi.org/10.1090/S0002-9939-1963-0153693-8
Article copyright: © Copyright 1963 American Mathematical Society