Marginal isomorphisms

Let G be a right module over a ring R and let QG denote the semi-primary classical right ring of quotients of EndR(G). Modules G and H are margimorphic if there are maps a:G→H and b:H→G such that ab and ba are regular elements in the respective endomorphism rings. The module H is called a marginal summand of G if G is margimorphic to H⊕H′ for some module H′. We study the existence and uniqueness of marginal summands of Gn for integers n>0 in terms of finitely generated projective right QG-modules. Some of these results extend to direct summands of Gn for integers n>0.