essentially retractable modules

we call a module  essentially retractable if homr for all essential submodules n of m. for a right fbn ring r, it is shown that: (i)  a non-zero module  is retractable (in the sense that homr for all non-zero ) if and only if certain factor modules of m are essentially retractable nonsingular modules over r modulo their annihilators. (ii)  a non-zero module  is essentially retractable if and only if there exists a prime ideal  such that homr. over semiprime right nonsingular rings, a nonsingular essentially retractable module is precisely a module with non-zero dual. moreover, over certain rings r, including right fbn rings, it is shown that a nonsingular module m with enough uniforms is essentially retractable if and only if there exist uniform retractable r-modules  and r-homomorphisms  with .