The Iwasawa algebra, classically, is the completed group ring , where is the subgroup of which is isomorphic to . The Iwasawa algebra is also isomorphic to the power series ring .
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