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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Reductions of ideals in Prüfer domains


Author: James H. Hays
Journal: Proc. Amer. Math. Soc. 52 (1975), 81-84
MSC: Primary 13F05
DOI: https://doi.org/10.1090/S0002-9939-1975-0376655-2
MathSciNet review: 0376655
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Abstract: All rings under consideration are Prüfer domains or valuation domains. We characterize the set of basic ideals and the set of $C$-ideals in an arbitrary valuation ring. Basic ideals were introduced in 1954 by Northcott and Rees. The concept of a $C$-ideal is, in a sense, directly opposite to that of a basic ideal. We then prove that a necessary and sufficient condition for every ideal in a domain $D$ to be basic is that $D$ be a one-dimensional Prüfer domain.


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Keywords: Reductions of ideals, basic, <IMG WIDTH="22" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$C$">-ideals, Pr&#252;fer domains, valuation rings, primary ideals, one-dimensional
Article copyright: © Copyright 1975 American Mathematical Society