Extensions of linearly McCoy rings
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A ring R is called linearly McCoy if whenever linear poly- nomials f(x), g(x) ∈ R[x]＼{0} satisfy f(x)g(x) = 0, there exist nonzero elements r, s ∈ 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.
Abstract
A ring R is called linearly McCoy if whenever linear poly- nomials f(x), g(x) ∈ R[x]＼{0} satisfy f(x)g(x) = 0, there exist nonzero elements r, s ∈ 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.
참고문헌 (17)
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