Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ANNIHILATING CONTENT IN POLYNOMIAL AND POWER SERIES RINGS

  • Abuosba, Emad (Department of Mathematics School of Science The University of Jordan) ;
  • Ghanem, Manal (Department of Mathematics School of Science The University of Jordan)
  • Received : 2018.10.19
  • Accepted : 2018.11.21
  • Published : 2019.09.01
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Abstract

Let R be a commutative ring with unity. If f(x) is a zero-divisor polynomial such that $f(x)=c_f f_1(x)$ with $c_f{\in}R$ and $f_1(x)$ is not zero-divisor, then $c_f$ is called an annihilating content for f(x). In this case $Ann(f)=Ann(c_f )$. We defined EM-rings to be rings with every zero-divisor polynomial having annihilating content. We showed that the class of EM-rings includes integral domains, principal ideal rings, and PP-rings, while it is included in Armendariz rings, and rings having a.c. condition. Some properties of EM-rings are studied and the zero-divisor graphs ${\Gamma}(R)$ and ${\Gamma}(R[x])$ are related if R was an EM-ring. Some properties of annihilating contents for polynomials are extended to formal power series rings.

Keywords

Acknowledgement

Supported by : The University of Jordan

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