such that for each prime ideal p, the completion of the localization Ap is equidimensional, i.e. for each minimal prime ideal q in the completion
[2] A Noetherian integral domain is quasi-unmixed if and only if it satisfies Nagata's altitude formula.
, the following are equivalent:[4][5] A Noetherian local ring
is said to be formally catenary if for every prime ideal
[6] As it turns out, this notion is redundant: Ratliff has shown that a Noetherian local ring is formally catenary if and only if it is universally catenary.
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