C.1 Standard bases
and let be a submodule of .
Note that for r=1 this means that is an ideal in .
Denote by the submodule of generated by the leading terms
of elements of , i.e. by
is called a standard basis of
- normal form:
, is called a normal
form if for any and any standard basis the following
then does not divide
for all .
(Note that such a function is not unique).
is called a normal form of with
- ideal membership:
For a standard basis of the following holds:
if and only if
- Hilbert function:
be a homogeneous module, then the Hilbert function
of (see below)
and the Hilbert function of the leading module