I was wondering whether people discuss "eigenvalues" of a module morphism $f:M\rightarrow M$. In the sense that $r$ is an "eigenvalue" of $f$ if there exists $m\in M\neq 0$ such that $f(m)=r\cdot m$.
The reason for this was for example whether one can discuss eigenvalues of the Laplacian defined on the appropriate homology group. More specifically when the homology is not freely generated, and is not akin to vector space.