Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON A CLASS OF PERFECT RINGS

  • Received : 2020.03.23
  • Accepted : 2020.04.21
  • Published : 2020.09.25
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Abstract

A module M is called ss-semilocal if every submodule U of M has a weak supplement V in M such that U∩V is semisimple. In this paper, we provide the basic properties of ss-semilocal modules. In particular, it is proved that, for a ring R, RR is ss-semilocal if and only if every left R-module is ss-semilocal if and only if R is semilocal and Rad(R) ⊆ Soc(RR). We define projective ss-covers and prove the rings with the property that every (simple) module has a projective ss-cover are ss-semilocal.

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References

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