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The integral closure need not be a Prüfer domain

Published online by Cambridge University Press:  26 February 2010

Robert Gilmer  and
Joseph F. Hoffmann
Robert Gilmer
Affiliation:
Florida State University, Tallahassee, Florida 32306.
Joseph F. Hoffmann
Affiliation:
Florida State University, Tallahassee, Florida 32306.
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Extract

Recent years have witnessed a significant development of the theory of Prüfer domains; there are many known characterizations of such domains within the class of integral domains with identity or the class of integrally closed domains—for example, see [6; Exer. 12, p. 93] or [10; Chap. 4]. E. Bastida and R. Gilmer have recorded in [4] a number of open questions concerning Prüfer domains that are of the following form:

If D is an integral domain with identity with property E, is the integral closure of D a Prüfer domain?

Specifically, the questions listed by Bastida and Gilmer were first raised in [13], [11], [7], and [12].

Type
Research Article
Information
Mathematika , Volume 21 , Issue 2 , December 1974 , pp. 233 - 238
Copyright
Copyright © University College London 1974

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References

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