  Motivated by some recent results of F. P\'erez and R. R.G connecting test
ideal of module closure operations and trace ideals, we investigate the test
ideal restricted to principal ideals corresponding to a module closure
operation of a torsion-free module $M$. We show that such a test ideal is
always a trace ideal, and moreover when $M$ is torsionless and faithful, then
it is the trace of the center of $\operatorname{End}_R(M)$. Some applications
are given.
