nLab Iwasawa algebra

Idea

The Iwasawa algebra, classically, is the completed group ring $\mathbb{Z}_{p}[[\Gamma]]$, where $\Gamma$ is the subgroup of $\Gal(\mathbb{Q}(\mu_{p^{}\infty})/\mathbb{Q})\cong \mathbb{Z}_{p}^{\times}$ which is isomorphic to $1+p\mathbb{Z}_{p}$. The Iwasawa algebra is also isomorphic to the power series ring $\mathbb{Z}_{p}[[T]]$.

Related concepts

• Iwasawa theory

References

• K. Ardakov, K. A. Brown, Ring-theoretic properties of Iwasawa algebras: a survey, Documenta Mathematica, Extra Volume: John H. Coates’ Sixtieth Birthday (2006), 7-33 link

See also:

• Wikipedia, Iwasawa_algebra