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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

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3.Gilmer, R. W., Multiplicative Ideal Theory (Marcel Dekker, 1972).Google Scholar
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5.Mori, S., Allgemeine Z.P.I.-ringe, J. Sci. Hirosima Univ. Ser. A. 10 (1940), 117–136.Google Scholar