 
Summary: Krull dimension of Iwasawa algebras
and some related topics.
Konstantin Ardakov,
Christ's College.
A dissertation submitted for the degree of
Doctor of Philosophy at the University of Cambridge.
March, 2004.
Abstract
Let G be a uniform prop group. We study certain algebraic properties of
the completed group algebra G = Zp[[G]] of G and of other related rings.
First, we consider the Krull dimension K(G) of G. We establish upper
and lower bounds on K(G) in terms of the QpLie algebra L(G) of G. We
show these bounds coincide in certain cases, including when L(G) is solvable,
and equal dim G + 1. We also show that K(G) < dim G + 1 when L(G)
is split simple over Qp. This answers a question of Brown, Hajarnavis and
McEacharn.
Next we study 1critical modules over the Fpversion of Iwasawa algebras,
G = Fp[[G]]. We show that the endomorphism ring of such a module M is
finite dimensional over Fp and that K(G/ Ann(M)) 2, whenever L(G) is
split semisimple over Qp. We also establish a useful technical result which
