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⊕-Cofinitely Supplemented Modules

Abstract

Let R be a ring and M a right R-module. M is called ⊕-cofinitely supplemented if every submodule N of M with M/N finitely generated has a supplement that is a direct summand of M. In this paper various properties of the ⊕-cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of ⊕-cofinitely supplemented modules is ⊕-cofinitely supplemented. (2) A ring R is semiperfect if and only if every free R-module is ⊕-cofinitely supplemented. In addition, if M has the summand sum property, then M is ⊕-cofinitely supplemented iff every maximal submodule has a supplement that is a direct summand of M.

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Correspondence to H. Çalişici.

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Çalişici, H., Pancar, A. ⊕-Cofinitely Supplemented Modules. Czech Math J 54, 1083–1088 (2004). https://doi.org/10.1007/s10587-004-6453-1

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Keywords

  • cofinite submodule
  • ⊕-cofinitely supplemented module