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A new characterization of Dedekind domains

Published online by Cambridge University Press:  18 May 2009

D. D. Anderson  and
E. W. Johnson
D. D. Anderson
Affiliation:
University of Iowa, Iowa City, Iowa 52242, USA
E. W. Johnson
Affiliation:
University of Iowa, Iowa City, Iowa 52242, USA
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Throughout this paper all rings are assumed commutative with identity. Among integral domains, Dedekind domains are characterized by the property that every ideal is a product of prime ideals. For a history and proof of this result the reader is referred to Cohen [2, pp. 31–32]. More generally, Mori [5] has shown that a ring has the property that every ideal is a product of prime ideals if and only if it is a finite direct product of Dedekind domains and special principal ideal rings (SPIRS). Rings with this property are called general Z.P.I.-rings.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 28 , Issue 2 , July 1986 , pp. 237 - 239
Copyright
Copyright © Glasgow Mathematical Journal Trust 1986

References

REFERENCES

1.Butts, H. S. and Gilmer, R. W., Primary ideals and prime power ideals, Canad. J. Math. 18 (1966), 1183–1195.CrossRefGoogle Scholar
2.Cohen, I. S., Commutative rings with restricted minimum condition, Duke Math. J. 17 (1950), 27–42.CrossRefGoogle Scholar
3.Gilmer, R. W., Multiplicative Ideal Theory (Marcel Dekker, 1972).Google Scholar
4.Levitz, K. B., A characterization of general Z.P.I.-rings II, Pacific J. Math. 42 (1972), 147–151.CrossRefGoogle Scholar
5.Mori, S., Allgemeine Z.P.I.-ringe, J. Sci. Hirosima Univ. Ser. A. 10 (1940), 117–136.Google Scholar