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The McCoy Condition on Skew Polynomial Rings
Communications in Algebra, 2009Based on a theorem of McCoy on commutative rings, Nielsen called a ring R right McCoy if, for any nonzero polynomials f(x), g(x) over R, f(x)g(x) = 0 implies f(x)r = 0 for some 0 ≠ r ∊ R. In this note, we consider a skew version of these rings, called σ-skew McCoy rings, with respect to a ring endomorphism σ.
Tai Keun Kwak, Muhittin Baser
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The McCoy Condition on Noncommutative Rings
Communications in Algebra, 2011McCoy proved in 1957 [12] that if a polynomial annihilates an ideal of polynomials over any ring then the ideal has a nonzero annihilator in the base ring. We first elaborate this McCoy's famous theorem further, expanding the inductive construction in the proof given by McCoy. From the proof we can naturally find nonzero c, with f(x)c = 0, in the ideal
, Yang Lee, Chan Yong Hong
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Zero-divisor placement, a condition of Camillo, and the McCoy property
Journal of Pure and Applied Algebra, 2020Let \(R\) be a (not necessarily commutative) ring and form \(R[x]\) the ring of polynomials over \(R\), where \(x\) commutes with the elements of \(R\). The ring \(R\) is a McCoy ring whenever for every \(f\), \(g\in R[x]\) with \(g\ne 0\) but \(fg=0\), then \(fr=0\) for some \(0\ne r\in R\).
Baeck, Jongwook +3 more
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The McCoy Condition on Ore Extensions
Communications in Algebra, 2013Nielsen [29] proved that all reversible rings are McCoy and gave an example of a semicommutative ring that is not right McCoy. When R is a reversible ring with an (α, δ)-condition, namely (α, δ)-compatibility, we observe that R satisfies a McCoy-type property, in the context of Ore extension R[x; α, δ], and provide rich classes of reversible ...
M. Habibi, A. Moussavi, A. Alhevaz
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On Rings Having McCoy-Like Conditions
Communications in Algebra, 2012In [41], Nielsen proves that all reversible rings are McCoy and gives an example of a semicommutative ring that is not right McCoy. At the same time, he also shows that semicommutative rings do have a property close to the McCoy condition. In this article we study weak McCoy rings as a common generalization of McCoy rings and weak Armendariz rings ...
A. Alhevaz, A. Moussavi, M. Habibi
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The McCoy condition on skew monoid rings
Asian-European Journal of Mathematics, 2017Let [Formula: see text] be an associative ring with identity, [Formula: see text] a monoid and [Formula: see text] a monoid homomorphism. When [Formula: see text] is a u.p.-monoid and [Formula: see text] is a reversible [Formula: see text]-compatible ring, then we observe that [Formula: see text] satisfies a McCoy-type property, in the context of skew
Paykan, Kamal, Moussavi, Ahmad
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The McCoy Condition on Skew Poincaré–Birkhoff–Witt Extensions
Communications in Mathematics and Statistics, 2019Let \(B\) be an associative ring with unity. \(B\) is called a (linearly) right McCoy ring, if the equality \(f(x)g(x) = 0\), where \(f(x), g(x)\) are (linear) polynomials in \(B\left[x\right] \setminus \left\{0\right\}\), implies that there exists a nonzero element \(c \in B\), such that \(f(x)c = 0\). Left McCoy rings are defined similarly.
Armando Reyes, Camilo Rodríguez
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Extensions of Rings Having McCoy Condition
Canadian Mathematical Bulletin, 2009AbstractLet R be an associative ring with unity. Then R is said to be a right McCoy ring when the equation f (x)g(x) = 0 (over R[x]), where 0 ≠ f (x), g(x) ∈ R[x], implies that there exists a nonzero element c ∈ R such that f (x)c = 0. In this paper, we characterize some basic ring extensions of right McCoy rings and we prove that if R is a right McCoy
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