Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Direct Sums of Lifting Modules and Internal Exchange Property

  • Dejun, Wu (Department of Applied Mathematics, Lanzhou University of Technology)
  • Received : 2003.11.19
  • Published : 2006.03.23
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Abstract

Let R be a ring with identity and let $M=M_1{\bigoplus}M_2$ be an amply supplemented R-module. Then it is proved that $M_i$ has ($D_1$) and is $M_j-^*ojective$ for $i{\neq}j$, i = 1, 2, if and only if for any coclosed submodule X of M, there exist $M\acute{_1}{\leq}M_1$ and $M\acute{_2}{\leq}M_2$ such that $M=X{\bigoplus}M\acute{_1}{\bigoplus}M\acute{_2}$.

Keywords

References

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