  The set of the first Hilbert coefficients of parameter ideals relative to a
module--its Chern coefficients--over a local Noetherian ring codes for
considerable information about its structure--noteworthy properties such as
that of Cohen-Macaulayness, Buchsbaumness, and of having finitely generated
local cohomology. The authors have previously studied the ring case. By
developing a robust setting to treat these coefficients for unmixed rings and
modules, the case of modules is analyzed in a more transparent manner. Another
series of integers arise from partial Euler characteristics and are shown to
carry similar properties of the module. The technology of homological degree
theory is also introduced in order to derive bounds for these two sets of
numbers.
