abstract_textpWe construct ascending chains of ideals in a commutative Noetherian ring R that reach arbitrary long sequences of equalities, however the chain does not become stationary at that point. For a regular ideal J in R, the Ratliff-Rush reduction number (r) over tilde (J) of J is the smallest positive integer n at which the chain J(2) : J subset of ... subset of J(n+1) : J(n) subset of ... becomes stationary. We construct ideals J so that such a chain reaches an arbitrary long sequence of equalities but (r) over tilde (J) is not being reached yet./p/abstract_text
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