Ring-theoretic properties of Iwasawa algebras: a survey

Abstract

This is a survey of the known properties of Iwasawa algebras, i.e., completed group rings of compact $p$-adic analytic groups with coefficients the ring ${\mathbb{Z}}_p$ of $p$-adic integers or the field ${\mathbb{F}}_p$ of $p$ elements. A number of open questions are also stated.