# ⊕-Cofinitely Supplemented Modules

Research paper by H. Çalişici, A. Pancar

Indexed on: 01 Dec '04Published on: 01 Dec '04Published in: Czechoslovak Mathematical Journal

#### 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.