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.