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Primary Ideals in Prüfer Domains

Published online by Cambridge University Press:  20 November 2018

Jack Ohm
Jack Ohm*
Affiliation:
University of Wisconsin, Madison, Wisconsin and Louisiana State University, Baton Rouge, Louisiana
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A Prüfer domain is an integral domain D with the property that for every proper prime ideal P of D the quotient ring DP is a valuation ring. Examples of such domains are valuation rings and Dedekind domains, a Dedekind domain being merely a noetherian Prüfer domain. The integral closure of the integers in an infinite algebraic extension of the rationals is another example of a Prüfer domain (5, p. 555, Theorem 8). This third example has been studied initially by Krull (4) and then by Nakano (8).

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1024 - 1030
Copyright
Copyright © Canadian Mathematical Society 1966

References

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