Abstract
A ring R is called linearly McCoy if whenever linear polynomials <TEX>$f(x)$</TEX>, <TEX>$g(x){\in}R[x</TEX><TEX>]</TEX><TEX>{\backslash}\{0\}$</TEX> satisfy <TEX>$f(x)g(x)=0$</TEX>, there exist nonzero elements <TEX>$r,s{\in}R$</TEX> such that <TEX>$f(x)r=sg(x)=0$</TEX>. 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.
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