## Fitting ideals for finitely presented algebraic dynamical systems.(English)Zbl 0972.22005

Let $$G$$ be a group acting by automorphisms on a compact abelian group $$X$$. The Pontryagin dual $$M=\widehat X$$, a discrete abelian group, becomes a module of the group ring $$R=\mathbb{Z}[G]$$ in a natural way. Algebraic properties of $$M$$ then reflect dynamical and topological properties of the action of $$G$$ on $$X$$. In the paper under consideration the case $$G=\mathbb{Z}^d$$ and $$M$$ noetherian is studied. The authors show how entropy, expansiveness and periodic point behaviour depend on the structure of the Fitting ideals of a finite free resolution of $$M$$.

### MSC:

 22D40 Ergodic theory on groups 37A15 General groups of measure-preserving transformations and dynamical systems
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