Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2013; 50(6): 1887-1903

Printed November 1, 2013

https://doi.org/10.4134/BKMS.2013.50.6.1887

Copyright © The Korean Mathematical Society.

McCoy condition on ideals of coefficients

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