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π-domains, overrings, and divisorial ideals

Published online by Cambridge University Press:  18 May 2009

D. D. Anderson
D. D. Anderson
Affiliation:
Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65201
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In this paper we study several generalizations of the concept of unique factorization domain. An integral domain is called a π-domain if every principal ideal is a product of prime ideals. Theorem 1 shows that the class of π-domains forms a rather natural subclass of the class of Krull domains. In Section 3 we consider overrings of π-domains. In Section 4 generalized GCD-domains are introduced: these form an interesting class of domains containing all Prüfer domains and all π-domains.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 19 , Issue 2 , July 1978 , pp. 199 - 203
Copyright
Copyright © Glasgow Mathematical Journal Trust 1978

References

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