  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
related to the augmentation ideals of closed normal subgroups are found. Some
information is obtained about the Krull and global dimensions of the
localisations. The results extend and complete work of A. Neumann and J. Coates
et al.
