  In the classical operator theory, there are several versions of spectra,
related to special classes of operators (Fredholm, semi-Fredholm, upper/lower
semi-Fredholm,etc.). We generalize these notions for adjointable operators on
Hilbert C*-modules replacing scalars by the center of the algebra, and show
that most relations between these spectra are still true for these generalized
versions. The relation between these spectra of an operator and those of its
compressions is also transferred to the case of Hilbert C*-modules.
