Depth of a Noetherian local ring
= Depth of a Noetherian local ring
{title2=$\operatorname{depth}R$}
The depth of a <Noetherian local ring> is the maximal length of an $R$-regular sequence in its maximal ideal. It is at most its <Krull dimension>. Quotienting by a nonzero divisor lowers depth by one. This invariant measures how many independent successive nonzero-divisor equations the local algebra supports.