Abstract
All rings under consideration are Prüfer domains or valuation domains. We characterize the set of basic ideals and the set of C C -ideals in an arbitrary valuation ring. Basic ideals were introduced in 1954 by Northcott and Rees. The concept of a C 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 D to be basic is that D D be a one-dimensional Prüfer domain.
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