대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제50권5호
  • /
  • Pages.1501-1511
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  • 2013
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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Extensions of linearly McCoy rings

  • Cui, Jian (Department of Mathematics Anhui Normal University) ;
  • Chen, Jianlong (Department of Mathematics Southeast University)
  • 투고 : 2012.04.08
  • 발행 : 2013.09.30
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초록

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.

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참고문헌

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