Annihilator conditions in endomorphism rings of modules

The characterization problem for endomorphism rings

“…On the other hand, a module A M is said to be intrinsically projective [2] when for every epimorphism f:M n^> L for L a submodule of M, and every homomorphism g: M -• L, there exists h: M -> M n such that f°h = g.…”

“…by Wolfson [20] in the 50s; and by Metelli and Salce [14] and Liebert [11,12,13] in the 70s. A more general result in this connection was obtained by Franzsen and Schultz [3,Theorem 3.2] in 1983: they provide a solution to the Characterization Problem for the class J[ of all the (locally) free i?-modules over rings R which satisfy the condition that each nonzero summand of a (locally) free .R-module is indecomposable if and only if it is isomorphic to R R. [2] Endomorphism rings 117…”