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X-LIFTING MODULES OVER RIGHT PERFECT RINGS

Chang, Chae-Hoon   (INFORMATION THCHNOLOGY MANPOWER DEVELOPMENT PROGRAM KYUNGPOOK NATIONAL UNIVERSITYUU0000096  );
  • 초록

    Keskin and Harmanci defined the family B(M,X) = ${A{\leq}M|{\exists}Y{\leq}X,{\exists}f{\in}Hom_R(M,X/Y),\;Ker\;f/A{\ll}M/A}$ . And Orhan and Keskin generalized projective modules via the class B(M, X). In this note we introduce X-local summands and X-hollow modules via the class B(M, X). Let R be a right perfect ring and let M be an X-lifting module. We prove that if every co-closed submodule of any projective module P contains Rad(P), then M has an indecomposable decomposition. This result is a generalization of Kuratomi and Chang's result [9, Theorem 3.4]. Let X be an R-module. We also prove that for an X-hollow module H such that every non-zero direct summand K of H with $K{\in}B$ (H, X), if $H{\oplus}H$ has the internal exchange property, then H has a local endomorphism ring.


  • 주제어

    right perfect ring .   lifting module .   exchange property.  

  • 참고문헌 (16)

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  • 이 논문을 인용한 문헌 (2)

    1. 2009. "" Bulletin of the Korean Mathematical Society = 대한수학회보, 46(6): 1069~1077     
    2. 2013. "" Kyungpook mathematical journal, 53(1): 37~47     

 저자의 다른 논문

  • Chang, Chae-Hoon (3)

    1. 2007 "PRIME IDEALS OF RINGS GRADED BY A COMMUTATIVE SEMIGROUP WHICH IS A NILPOTENT EXTENSION OF A GROUP" Honam mathematical journal = 호남수학학술지 29 (4): 667~679    
    2. 2008 "Finitely Generated Modules over Semilocal Rings and Characterizations of (Semi-)Perfect Rings" Kyungpook mathematical journal 48 (1): 143~154    
    3. 2009 "ON THE DECOMPOSITION OF EXTENDING LIFTING MODULES" Bulletin of the Korean Mathematical Society = 대한수학회보 46 (6): 1069~1077    

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