Summary: Krull dimension of Iwasawa algebras
and some related topics.
A dissertation submitted for the degree of
Doctor of Philosophy at the University of Cambridge.
Let G be a uniform pro-p 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 Qp-Lie 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
Next we study 1-critical modules over the Fp-version 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