Ardakov, K.; Brown, K.A.

Ring-theoretic properties of Iwasawa algebras: a survey.

Doc. Math. (Bielefeld) Extra Vol. John H. Coates' Sixtieth Birthday, 7-33 (2006)


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.

Mathematics Subject Classification

16L30, 16S34, 16P50, 11R23, 20E18, 20C07, 16P40


Iwasawa algebras, maximal orders, dimensions, localisations, compact $p$-adic analytic groups, completed group rings