Generalized “stacked bases” theorem for modules over semiperfect rings

Abstract

The history of generalized “stacked bases” theorem origins from the result of Hill and Megibben on abelian groups. We extend this theorem for modules over semiperfect rings and as a consequence we show that for a submodule H of a projective module G over a semiperfect ring, the following conditions are equivalent: there exists a decomposition into a direct sum of indecomposable modules Pi , such that G/H is a direct sum of a family of modules, isomorphic to factor modules of principal indecomposable modules.