Iwasawa algebra of a Zp-extension
= Iwasawa algebra of a Zp-extension
{c}
{title2=$\Lambda=\mathbb Z_p[[\Gamma]]\cong\mathbb Z_p[[T]]$}
Choose a topological generator $\gamma$ of the <Galois group> of a <Zp-extension> and set $T=\gamma-1$. The <completed group algebra> becomes the <formal power series ring> $\mathbb Z_p[[T]]$, a two-dimensional complete regular local <integral domain> with maximal ideal $(p,T)$. Its finite-layer quotient is $\Lambda/((1+T)^{p^n}-1)\cong\mathbb Z_p[\Gamma/\Gamma^{p^n}]$.