Extensions of linearly McCoy rings
Bull. Korean Math. Soc. 2013 Vol. 50, No. 5, 1501-1511
https://doi.org/10.4134/BKMS.2013.50.5.1501
Published online September 1, 2013
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
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