McCoy condition on ideals of coefficients
Bull. Korean Math. Soc. 2013 Vol. 50, No. 6, 1887-1903
https://doi.org/10.4134/BKMS.2013.50.6.1887
Published online November 1, 2013
Jeoung Soo Cheon, Chan Huh, Tai Keun Kwak, and Yang Lee
Pusan National University, Pusan National University, Daejin University, Pusan National University
Abstract : We continue the study of McCoy condition to analyze zero-dividing polynomials for the constant annihilatorsin 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.
Keywords : ideal-$\pi$-McCoy ring, strongly McCoy ring, $\pi$-McCoy ring, polynomial ring, matrix ring, the classical right quotient ring
MSC numbers : 16D25, 16S36
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