 
Summary: Krull dimension of Iwasawa algebras
Konstantin Ardakov
1 Introduction
Let G be a compact padic Lie group. In the recent years, there has been an
increased amount of interest in completed group algebras (Iwasawa algebras)
G = Z p [[G]] := lim
N/oGZ p [G=N ];
for example, because of their connections with number theory and arithmetic
geometry; see the paper by Coates, Schneider and Sujatha ([4]) for more details.
When G is a uniform prop group, G is a concrete example of a complete
local Noetherian ring (noncommutative, in general) with good homological prop
erties: it is known that G has nite global dimension and is an Auslander regu
lar ring. Thus, G falls into the class of rings studied by Brown, Hajarnavis and
MacEacharn in [1]. There they consider various properties of Noetherian rings
R of nite global dimension, including the Krull(GabrielRentschler) dimension
K(R)  a moduletheoretic dimension which measures how far R is from being
Artinian. They also posed the following question:
Question ([1], Section 5). Let R be a local right Noetherian ring, whose
Jacobson radical satises the ArtinRees property. Is the Krull dimension of R
always equal to the global dimension of R?
