Extensions of linearly McCoy rings

Title & Authors
Extensions of linearly McCoy rings
Cui, Jian; Chen, Jianlong;

Abstract
A ring R is called linearly McCoy if whenever linear polynomials $\small{f(x)}$, $\small{g(x){\in}R[x}$$\small{]}$$\small{{\backslash}\{0\}}$ satisfy $\small{f(x)g(x)=0}$, there exist nonzero elements $\small{r,s{\in}R}$ such that $\small{f(x)r=sg(x)=0}$. 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;
Language
English
Cited by
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