 
Summary: PRIMENESS, SEMIPRIMENESS AND LOCALISATION IN
IWASAWA ALGEBRAS
KONSTANTIN ARDAKOV AND KENNETH A. BROWN
Preface. Necessary and suÆcient conditions are given for the completed
group algebras of a compact p adic analytic group with coeÆcient ring the
padic integers or the eld of p elements to be prime, semiprime and a domain.
Necessary and suÆcient conditions for the localisation at semiprime ideals re
lated to the augmentation ideals of closed normal subgroups are found. Some
information is obtained about the Krull and global dimensions of the local
isations. The results extend and complete work of A. Neumann [12] and J.
Coates et al [5].
1. Introduction
1.1. In recent years there has been increasing interest in noncommutative Iwasawa
algebras. These are the completed group algebras
G := lim
Z p [G=U ];
where Z p denotes the ring of p adic integers, G is a compact p adic analytic group,
and the inverse limit is taken over the open normal subgroups of G. Closely related
is the epimorphic
image
