= Cyclotomic Milnor square
{title2=$\mathbb Z[C_p]=\mathbb Z\times_{\mathbb F_p}\mathbb Z[\zeta_p]$}
Evaluation of the cyclic generator at $1$ and at a primitive $p$th root gives the displayed <pullback>. The maps to the common <field> reduce integers modulo $p$ and set $\zeta_p=1$. If a representative <polynomial> for the second component has value $c$ at one, adding an integer multiple of $\Phi_p$ adjusts that value by a multiple of $p$ without changing the second component. This proves surjectivity onto compatible pairs.
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