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Research Article

Generalized “stacked bases” theorem for modules over semiperfect rings

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Pages 2597-2605 | Received 25 Feb 2020, Accepted 09 Nov 2020, Published online: 10 Feb 2021
 

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:

  1. there exists a decomposition G=iIPi into a direct sum of indecomposable modules Pi, such that H=iI(PiH);

  2. G/H is a direct sum of a family of modules, isomorphic to factor modules of principal indecomposable modules.

Additional information

Funding

The first author is partially supported by the RFFI under Grant No. 20-01-00030.

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