Theorem 3.7 in the chapter on ring extension on page 352 of the latest edition of Lang's "Algebra" appears redundant in its phrasing to me. Specifically, if $g_s$ is a polynomial of total degree $< d_s$, isn't any pure power of one of its variables $Z_s$ automatically occuring with a power strictly less than $d_s$?
What could he have meant with this statement? (If it just plain redundant and no deeper meaning to it, it would also be good to be ensured.)