Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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WEAKLY TRIPOTENT RINGS

  • Breaz, Simion (Faculty of Mathematics and Computer Science Babes-Bolyai University) ;
  • Cimpean, Andrada (Faculty of Mathematics and Computer Science Babes-Bolyai University)
  • Received : 2017.07.28
  • Accepted : 2018.01.29
  • Published : 2018.07.31
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Abstract

We study the class of rings R with the property that for $x{\in}R$ at least one of the elements x and 1 + x are tripotent. We prove that a commutative ring has this property if and only if it is a subring of a direct product $R_0{\times}R_1{\times}R_2$ such that $R_0/J(R_0){\cong}{\mathbb{z}}_2$, for every $x{\in}J(R_0)$ we have $x^2=2x$, $R_1$ is a Boolean ring, and $R_3$ is a subring of a direct product of copies of ${\mathbb{z}}_3$.

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References

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