Bulletin of the
Korean Mathematical Society
BKMS

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

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Bull. Korean Math. Soc. 2013; 50(5): 1501-1511

Printed September 1, 2013

https://doi.org/10.4134/BKMS.2013.50.5.1501

Copyright © The Korean Mathematical Society.

Extensions of linearly McCoy rings

Jian Cui and Jianlong Chen

Anhui Normal University, Southeast University

Abstract

A ring $R$ is called linearly McCoy if whenever linear polynomials $f(x),~g(x) \in R[x]\backslash \{0\}$ satisfy $f(x)g(x)=0$, there exist nonzero elements $r,~s\in R$ such that $f(x)r=sg(x)=0$. In this paper, extension properties of linearly McCoy rings are investigated. We prove that the polynomial ring over a linearly McCoy ring need not be linearly McCoy. It is shown that if there exists the classical right quotient ring $Q$ of a ring $R$, then $R$ is right linearly McCoy if and only if so is $Q$. Other basic extensions are also considered.

Keywords: polynomial ring, linearly McCoy ring, matrix ring, semi-commutative ring, McCoy ring

MSC numbers: Primary 16U80; Secondary 16S99