C.4 Characteristic sets
Let be the lexicographical ordering on with . For let lvar() (the leading variable of ) be the largest variable in , i.e., if for some then lvar.
Moreover, let ini . The pseudoremainder of with respect to is defined by the equality with and minimal.
A set is called triangular if . Moreover, let , then is called a triangular system, if is a triangular set such that does not vanish on .
is called irreducible if for every there are no
,, such that
Furthermore, is called irreducible if is irreducible.
The main result on triangular sets is the following: Let , then there are irreducible triangular sets such that where . Such a set is called an irreducible characteristic series of the ideal .