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 $\Bbb Z_p$ of $p$-adic integers or the field $\Bbb F_p$ of $p$ elements. A number of open questions are also stated.