Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Weakly np-Injective Rings and Weakly C2 Rings

  • Wei, Junchao (Junchao Wei and Jianhua Chen School of Mathematics, Yangzhou University) ;
  • Che, Jianhua (Junchao Wei and Jianhua Chen School of Mathematics, Yangzhou University)
  • Received : 2008.09.17
  • Accepted : 2010.12.27
  • Published : 2011.03.31
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Abstract

A ring R is called left weakly np- injective if for each non-nilpotent element a of R, there exists a positive integer n such that any left R- homomorphism from $Ra^n$ to R is right multiplication by an element of R. In this paper various properties of these rings are first developed, many extending known results such as every left or right module over a left weakly np- injective ring is divisible; R is left seft-injective if and only if R is left weakly np-injective and $_RR$ is weakly injective; R is strongly regular if and only if R is abelian left pp and left weakly np- injective. We next introduce the concepts of left weakly pp rings and left weakly C2 rings. In terms of these rings, we give some characterizations of (von Neumann) regular rings such as R is regular if and only if R is n- regular, left weakly pp and left weakly C2. Finally, the relations among left C2 rings, left weakly C2 rings and left GC2 rings are given.

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References

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