Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Direct Sums of Extending Modules

LIU ZHONGKUI

  • Published : 20030000

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Abstract

Let M and N be left R-modules. N is called M-ep-injective if N is essentially M-injective and pseudoly M-injective. An example is given to show that M-ep-injectivity is a non-trivial generalization of M-injectivity. We show that any direct sum of relatively ep-injective extending left R-modules of finite length is special extending. It is also proved that the direct sum M=ⓧi∈I$M_i$ of left R-modules $M_i$ (i∈I, I≥2) is extending if and only if there exist i ≠ j in I such that every closed submodule K of M with K ∩ $M_i{\le}_e$K or K ∩ $M_j{\le}_e$ K or K ∩ $M_i$= K ∩ $M_j$ = 0 is a direct summand

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References

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