The associated graded module of a module 
over a commutative unit ring 
, with respect to a filtration
 |
(1)
|
of ideals of 
,
is
 |
(2)
|
which is a graded module over the associated graded ring 
. Addition is defined componentwise. For 
and 
,
the residue class of 
in 
sends the residue class
of 
in 
to the residue class of 
in 
.
If 
is a proper ideal of 
, then the notation 
indicates the associated graded module of 
with respect to the 
-adic filtration of 
,
 |
(3)
|
