Linearly compact modules and almost maximal rings -- h-Local domains -- Valuation rings and Bezout rings -- Basic facts about FGC rings and the local case -- Further facts about FGC rings and Torch rings -- The Zariski and Patch topologies of the spectrum of a ring -- The Stone-Cech compactification of N -- Relating topology to the decomposition of modules -- The main theorem -- Valuations -- Long power series rings -- Maximally complete valuation domains -- Examples of maximal valuation rings -- Examples of almost maximal Bezout domains -- Examples of Torch rings