  The structure of uniformly continuous quantum Markov semigroups with atomic
decoherence-free subalgebra is established providing a naturaldecomposition of
a Markovian open quantum system into its noiseless (decoherence-free) and
irreducible (ergodic) components. This leads to a new characterisation of the
structure of invariant states and a new method for finding decoherence-free
subsystems and subspaces. Examples are presented to illustrate these results.
