  By studying the reciprocity property of linear Diophantine systems in light
of Malcev-Neumann series, we present in this paper a new approach to and a
generalization of Stanley's monster reciprocity theorem. A formula for the
"error term" is given in the case when the system does not have the reciprocity
property. We also give a short proof of Stanley's reciprocity theorem for
linear homogeneous Diophantine systems.
