The module depth of a nonzero finitely generated module 
over a Noetherian local
ring 
is the largest length of an 
-regular sequence contained in 
. Such a sequence 
, ..., 
has the property that multiplication by 
is injective on 
and the final quotient
module is nonzero. This extends ring regular
sequence from 
to a module (Bruns and Herzog 1998).
The depth is at most the Krull dimension 
. For 
, it is the depth of the ring. A
Cohen-Macaulay ring that is a local
ring has depth equal to its Krull dimension.
