Kyungpook Mathematical Journal

  • 제55권2호
  • /
  • Pages.289-300
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  • 2015
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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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Some Results on δ-Semiperfect Rings and δ-Supplemented Modules

  • ABDIOGLU, CIHAT (Department of Mathematics, Karamanoglu Mehmetbey University) ;
  • SAHINKAYA, SERAP (Department of Mathematics, Gebze Institute of Technology)
  • 투고 : 2014.04.28
  • 심사 : 2014.10.17
  • 발행 : 2015.06.23
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초록

In [9], the author extends the definition of lifting and supplemented modules to ${\delta}$-lifting and ${\delta}$-supplemented by replacing "small submodule" with "${\delta}$-small submodule" introduced by Zhou in [13]. The aim of this paper is to show new properties of ${\delta}$-lifting and ${\delta}$-supplemented modules. Especially, we show that any finite direct sum of ${\delta}$-hollow modules is ${\delta}$-supplemented. On the other hand, the notion of amply ${\delta}$-supplemented modules is studied as a generalization of amply supplemented modules and several properties of these modules are given. We also prove that a module M is Artinian if and only if M is amply ${\delta}$-supplemented and satisfies Descending Chain Condition (DCC) on ${\delta}$-supplemented modules and on ${\delta}$-small submodules. Finally, we obtain the following result: a ring R is right Artinian if and only if R is a ${\delta}$-semiperfect ring which satisfies DCC on ${\delta}$-small right ideals of R.

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참고문헌

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