Graded shift
= Graded shift
{title2=$M(-a)$}
The graded shift $M(-a)$ is the same underlying <module> with $M(-a)_d=M_{d-a}$. Thus $S(-a)$ has a free generator in degree $a$. Its <Hilbert series> is $t^aH_M(t)$, and multiplication by a homogeneous element of degree $a$ becomes a degree-preserving map $M(-a)\to M$.