Depth of an ideal

Definition

Let $R$ be a commutative unital ring and $I$ be an ideal inside $R$. The depth of $I$ is the length of a maximal regular sequence in $I$. A regular sequence is a sequence of elements where each element is not a zero divisor in the ideal spanned by the preceding elements.

A related notion is depth of an ideal on a module, where we replace zero divisor by zero divisor on the module.