 Depth of a Noetherian local ring

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.