I am reading a few texts on Castelnuovo-Mumford regularity. If I understand correctly, almost all of them say:
If $I$ is a homogeneous ideal in $k[X_0,...,X_n]$ where $k$ is algebraically closed and $S$ is a generating set of $I$, then the regularity of $I$ is at least equal to the maximal degree of any element in $S$. Is this correct? Is there a good reference for this or is it obvious?