= 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 in the <maximal ideal> lowers depth by one. A unit is excluded from this assertion, since its quotient is the zero ring. This invariant measures how many independent successive nonzero-divisor equations the local algebra supports.
Back to article page
