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PRIMENESS, SEMIPRIMENESS AND LOCALISATION IN IWASAWA ALGEBRAS
 

Summary: PRIMENESS, SEMIPRIMENESS AND LOCALISATION IN
IWASAWA ALGEBRAS
KONSTANTIN ARDAKOV AND KENNETH A. BROWN
Preface. Necessary and sufficient conditions are given for the completed
group algebras of a compact p-adic analytic group with coefficient ring the
p-adic integers or the field of p elements to be prime, semiprime and a domain.
Necessary and sufficient 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
-
Zp[G/U],
where Zp 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 G of G,

  

Source: Ardakov, Konstantin - School of Mathematical Sciences, University of Nottingham

 

Collections: Mathematics