Study of Subhomomorphic Property to a Ring

Let m and n be two non-zero right r-modules, m is called subhomomorphic to n in case there exist r−homomorphisms f : m rightarrow n, g : n rightarrow m such that gof is non-zero, and m is called strongly subhomomorphic to n in case there exist homomorphisms f : m rightarrow n, g : n rightarrow m such that both fog and gof are non-zero. after establishing some basic properties of (strongly) subhomomorphic to a ring, it is shown that for a nonsingular ring r the class of injective right r-modules are subhomomorphic to r if and only if r is a semisimple ring