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ON A GENERALIZATION OF ⊕-SUPPLEMENTED MODULES

  • Turkmen, Burcu Nisanci (Faculty of Sciences and Arts, Amasya University) ;
  • Davvaz, Bijan (Department of Mathematics, Yazd University)
  • Received : 2018.11.29
  • Accepted : 2019.01.09
  • Published : 2019.09.25

Abstract

We introduce FI-${\oplus}$-supplemented modules as a proper generalization of ${\oplus}$-supplemented modules. We prove that; (1) every finite direct sum of FI-${\oplus}$-supplemented R-modules is an FI-${\oplus}$-supplemented R-module for any ring R ; (2) if every left R-module is FI-${\oplus}$-supplemented over a semilocal ring R, then R is left perfect; (3) if M is a finitely generated torsion-free uniform R-module over a commutative integrally closed domain such that every direct summand of M is FI-${\oplus}$-supplemented, then M is a direct sum of cyclic modules.

Keywords

fully invariant submodule;supplement;${\oplus}$-supplemented module;FI-${\oplus}$-supplemented module;left perfect ring

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