On Cohen–Macaulay Rings of Invariants

We investigate the transfer of the Cohen–Macaulay property from a commutative ring to a subring of invariants under the action of a finite group. Our point of view is ring theoretic and not a priori tailored to a particular type of group action. As an illustration, we discuss the special case of multiplicative actions, that is, actions on group algebras k[Zn] via an action on Zn.