MCCOY CONDITION ON IDEALS OF COEFFICIENTS

Title & Authors
MCCOY CONDITION ON IDEALS OF COEFFICIENTS
Cheon, Jeoung Soo; Huh, Chan; Kwak, Tai Keun; Lee, Yang;

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-$\small{{\pi}}$-McCoy rings, extending known results related to McCoy condition. It is shown that the class of ideal-$\small{{\pi}}$-McCoy rings contains both strongly McCoy rings whose non-regular polynomials are nilpotent and 2-primal rings. We also investigate relations between the ideal-$\small{{\pi}}$-McCoy property and other standard ring theoretic properties. Moreover we extend the class of ideal-$\small{{\pi}}$-McCoy rings by examining various sorts of ordinary ring extensions.
Keywords
ideal-$\small{{\pi}}$-McCoy ring;strongly McCoy ring;$\small{{\pi}}$-McCoy ring;poly-nomial ring;matrix ring;the classical right quotient ring;
Language
English
Cited by
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