Given a module 
over a commutative unit ring 
and a filtration
 |
(1)
|
of ideals of 
, the Rees module of 
with respect to 
is
 |
(2)
|
which is the set of all formal polynomials in the variable 
in which the coefficient of 
is of the form 
, where 
and 
. It is a graded module
over the Rees ring 
.
The subscript 
distinguishes it from the so-called extended Rees module, defined as
 |
(3)
|
where 
for all 
.
This module includes all polynomials containing negative powers of 
.
If 
is a proper
ideal of 
,
the notation 
(or 
) indicates the (extended) Rees
module of 
with respect to the 
-adic
filtration.
