  Classically the Chern-classes of a locally free coherent A-module W are
defined using the curvature of a connection. If we more generally consider the
problem of defining Chern-classes where W is a coherent A-module, a connection
might not exist. In this paper we use the linear Lie-algebroid of W, where W is
any coherent A-module of finite presentation, to define the first Chern-class
of W. We also do explicit calculations of Chern-classes for maximal
Cohen-Macaulay modules on isolated hypersurface-singularities and 2-dimensional
quotient-singularities.
