  Let (X,\sigma) be a symplectic space admitting a complex structure and let
R(X,\sigma) be the corresponding resolvent algebra, i.e. the C*-algebra
generated by the resolvents of selfadjoint operators satisfying canonical
commutation relations associated with (X,\sigma). In previous work this algebra
was shown to provide a convenient framework for the analysis of quantum
systems. In the present article its mathematical properties are elaborated with
emphasis on its ideal structure. It is shown that R(X,\sigma) is always nuclear
and, if X is finite dimensional, also of type I (postliminal). In the latter
case dim(X) labels the isomorphism classes of the corresponding resolvent
algebras. For X of arbitrary dimension, principal ideals are identified which
are the building blocks for all other ideals. The maximal and minimal ideals of
the resolvent algebra are also determined.
