This highly interesting, well-written and timely paper applies Saharon Shelah’s ingenious Black Box to the simultaneous investigation of endomorphism algebras \(End_ RG\) of torsion-free, torsion, and mixed R- modules G where R is a commutative ring with identity. \(End_ RG\) is considered as equipped with the finite topology. A central role plays the ideal Ines G of all ”inessential” endomorphisms of G. Conditions are given for a topological R-algebra A which guarantee the existence of a torsion-free, torsion, or mixed R-module G with the property that A can be topologically embedded in \(End_ RG\) in such a way that \(End_ RG=A\oplus Ines G\). The cardinality of the class of non-isomorphic G with this property is considered as well as the existence of ”maximal rigid systems”. Applications are given. Of special interest is an appendix outlining ”The Black Box”.