Kyungpook Mathematical Journal

  • 제56권4호
  • /
  • Pages.1069-1083
  • /
  • 2016
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  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Some Characterizations of Modules via Essentially Small Submodules

  • Le, Van Thuyet (Department of Mathematics, Hue University) ;
  • Phan, Hong Tin (Department of Mathematics, Hue University's College of Education)
  • 투고 : 2015.03.12
  • 심사 : 2016.05.11
  • 발행 : 2016.12.23
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초록

In this paper, the structure of e-local modules and classes of modules via essentially small are investigated. We show that the following conditions are equivalent for a module M: (1) M is e-local; (2) $Rad_e(M)$ is a maximal submodule of M and every proper essential submodule of M is contained in a maximal submodule; (3) M has a unique essential maximal submodule and every proper essential submodule of M is contained in a maximal submodule.

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참고문헌

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