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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).

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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