Extensions of uniserial modules

Abstract

Let R be any ring and let 0 → A → B → C → 0 be an exact sequence of R-modules which does not split with A and C uniserial. Then either B is indecomposable or B has a decomposition of the form B = B1 ⊕ B2 where B1 and B2 are indecomposable and at least one of them is uniserial. Mathematics Subject Classification (2010).Primary: 16D10; Secondary: 16G20.