Kyungpook Mathematical Journal

  • 제60권1호
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  • Pages.45-51
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  • 2020
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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On Generalized FI-extending Modules

  • Yucel, Canan Celep (Department of Mathematics, Faculty of Arts and Sciences, Pamukkale University)
  • 투고 : 2016.06.03
  • 심사 : 2019.12.03
  • 발행 : 2020.03.31
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초록

A module M is called FI-extending if every fully invariant submodule of M is essential in a direct summand of M. In this work, we define a module M to be generalized FI-extending (GFI-extending) if for any fully invariant submodule N of M, there exists a direct summand D of M such that N ≤ D and that D/N is singular. The classes of FI-extending modules and singular modules are properly contained in the class of GFI-extending modules. We first develop basic properties of this newly defined class of modules in the general module setting. Then, the GFI-extending property is shown to carry over to matrix rings. Finally, we show that the class of GFI-extending modules is closed under direct sums but not under direct summands. However, it is proved that direct summands are GFI-extending under certain restrictions.

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참고문헌

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