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