I am reading the commutative algebra book by W. Bruns and H. Herzog. I am stuck at the Corollary 4.1.8 which comes from lemma 4.1.7. Actually in the corollary $d=0$ case does not come from the previous lemma. It requires an independent proof. So far it is clear to me that Hilbert polynomial is the $0$ polynomial. What I couldn't understand is $Q_M(1) $ is non zero in this case. I need some help. Many many thanks.