  We consider a class of algebraic dynamical systems introduced by Kitchens and
Schmidt. Under a weak finiteness condition -- the Descending Chain Condition --
the dual modules have finite presentations. Using methods from commutative
algebra we show how the dynamical properties of the system may be deduced from
the Fitting ideals of a finite free resolution of the finitely presented
module. The entropy and expansiveness are shown to depend only on the first
Fitting ideal (and certain multiplicity data) which gives an easy computation:
in particular, no syzygy modules need to be computed. For `square'
presentations (in which the number of generators is equal to the number of
relations) all the dynamics is visible in the first Fitting ideal and certain
multiplicity data, and we show how the dynamical properties and periodic point
behaviour may be deduced from the determinant of the matrix of relations.
