Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MCCOY CONDITION ON IDEALS OF COEFFICIENTS

  • Cheon, Jeoung Soo (Department of Mathematics Pusan National University) ;
  • Huh, Chan (Department of Mathematics Pusan National University) ;
  • Kwak, Tai Keun (Department of Mathematics Daejin University) ;
  • Lee, Yang (Department of Mathematics Education Pusan National University)
  • Received : 2012.04.10
  • Published : 2013.11.30
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Abstract

We continue the study of McCoy condition to analyze zero-dividing polynomials for the constant annihilators in the ideals generated by the coefficients. In the process we introduce the concept of ideal-${\pi}$-McCoy rings, extending known results related to McCoy condition. It is shown that the class of ideal-${\pi}$-McCoy rings contains both strongly McCoy rings whose non-regular polynomials are nilpotent and 2-primal rings. We also investigate relations between the ideal-${\pi}$-McCoy property and other standard ring theoretic properties. Moreover we extend the class of ideal-${\pi}$-McCoy rings by examining various sorts of ordinary ring extensions.

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References

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