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Bull. Korean Math. Soc. 2017; 54(2): 521-541

Online first article January 4, 2017      Printed March 31, 2017

https://doi.org/10.4134/BKMS.b160160

Copyright © The Korean Mathematical Society.

An elaboration of annihilators of polynomials

Jeoung Soo Cheon, Hong Kee Kim, Nam Kyun Kim, Chang Ik Lee, Yang Lee, and Hyo Jin Sung

Pusan National University, Gyeongsang National University, Hanbat National University, Pusan National University, Pusan National University, Pusan National University

Abstract

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In this note we elaborate first on well-known theorems for annihilators of polynomials over IFP rings by investigating the concrete shapes of nonzero constant annihilators. We consider next a generalization of IFP which preserves Abelian property, in relation with annihilators of polynomials, observing the basic structure of rings satisfying such condition.

Keywords: IFP ring, $\pi$-IFP ring, polynomial ring, constant annihilator of polynomial, Abelian ring, locally finite ring

MSC numbers: 16U80, 16S36

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