Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Weak F I-extending Modules with ACC or DCC on Essential Submodules

  • Tercan, Adnan (Department of Mathematics, Hacettepe University, Beytepe Campus) ;
  • Yasar, Ramazan (Hacettepe-ASO 1.OSB Vocational School, Hacettepe University)
  • Received : 2020.04.19
  • Accepted : 2020.12.14
  • Published : 2021.06.30
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Abstract

In this paper we study modules with the W F I+-extending property. We prove that if M satisfies the W F I+-extending, pseudo duo properties and M/(Soc M) has finite uniform dimension then M decompose into a direct sum of a semisimple submodule and a submodule of finite uniform dimension. In particular, if M satisfies the W F I+-extending, pseudo duo properties and ascending chain (respectively, descending chain) condition on essential submodules then M = M1 ⊕ M2 for some semisimple submodule M1 and Noetherian (respectively, Artinian) submodule M2. Moreover, we show that if M is a W F I-extending module with pseudo duo, C2 and essential socle then the quotient ring of its endomorphism ring with Jacobson radical is a (von Neumann) regular ring. We provide several examples which illustrate our results.

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References

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