Definition 111.18.1. A Noetherian ring A is said to be catenary if for any triple of prime ideals {\mathfrak p}_1 \subset {\mathfrak p}_2 \subset {\mathfrak p}_3 we have
Here ht(\mathfrak p/\mathfrak q) means the height of \mathfrak p/\mathfrak q in the ring A/\mathfrak q. In a formula
A topological space X is catenary, if given T \subset T' \subset X with T and T' closed and irreducible, then there exists a maximal chain of irreducible closed subsets
and every such chain has the same (finite) length.
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