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.
Jian Cui and Jianlong Chen
Anhui Normal University, Southeast University
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
2023; 60(5): 1321-1334
2022; 59(3): 529-545
2019; 56(5): 1257-1272
2019; 56(4): 993-1006
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd