Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON U-GROUP RINGS

  • Osba, Emad Abu (Department of Mathematics School of Science The University of Jordan) ;
  • Al-Ezeh, Hasan (Department of Mathematics School of Science The University of Jordan) ;
  • Ghanem, Manal (Department of Mathematics School of Science The University of Jordan)
  • Received : 2017.09.20
  • Accepted : 2017.12.21
  • Published : 2018.10.31
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Abstract

Let R be a commutative ring, G be an Abelian group, and let RG be the group ring. We say that RG is a U-group ring if a is a unit in RG if and only if ${\epsilon}(a)$ is a unit in R. We show that RG is a U-group ring if and only if G is a p-group and $p{\in}J(R)$. We give some properties of U-group rings and investigate some properties of well known rings, such as Hermite rings and rings with stable range, in the presence of U-group rings.

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References

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