# Extensions of linearly McCoy rings

• Cui, Jian ;
• Chen, Jianlong
• Published : 2013.09.30
• 29 9

#### 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

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