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.