• Title, Summary, Keyword: linearly McCoy ring

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Extensions of linearly McCoy rings

  • Cui, Jian;Chen, Jianlong
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.5
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    • pp.1501-1511
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    • 2013
  • 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.