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Abelian right McCoy rings and related notions
Sao Paulo Journal of Mathematical Sciences, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Henry Chimal-Dzul +2 more
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A note on Brown—McCoy radicals ofΓ-rings
Periodica Mathematica Hungarica, 1987In [1] we defined the Brown—McCoy radical,B(M), of aΓ-ringM. In this note we show thatB is a special radical. The simplicial radical, defined by Kyuno [4] forΓ-rings with left and right unities, is extended to arbitraryΓ-rings. The simplicial radicalS is shown to be a generalization of the Brown—McCoy radical of a ring. In general,B(M) ≠ S(M).
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Semi-commutativity and the McCoy condition
Journal of Algebra, 2006 We prove that all reversible rings are McCoy, generalizing the fact that both commutative and reduced rings are McCoy. We then give an example of a semi-commutative ring that is not right McCoy.
Nielsen, Pace P.
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Algebra Colloquium, 2009
A ring R is called right McCoy if whenever polynomials f(x), g(x) ∈ R[x]∖{0} satisfy f(x)g(x)=0, there exists a nonzero r ∈ R such that f(x)r=0. We continue in this paper the study of right McCoy rings by Nielsen [8]. We first consider properties and basic extensions of right McCoy rings, providing many examples in the process. Next, we show that if R
Zhao, Renyu, Liu, Zhongkui
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A ring R is called right McCoy if whenever polynomials f(x), g(x) ∈ R[x]∖{0} satisfy f(x)g(x)=0, there exists a nonzero r ∈ R such that f(x)r=0. We continue in this paper the study of right McCoy rings by Nielsen [8]. We first consider properties and basic extensions of right McCoy rings, providing many examples in the process. Next, we show that if R
Zhao, Renyu, Liu, Zhongkui
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On right McCoy rings and right McCoy rings relative to u.p.-monoids
Communications in Contemporary Mathematics, 2015In this paper, we prove that all right duo rings are right McCoy relative to any u.p.-monoid. We also show that for any nontrivial u.p.-monoid M, the class of right McCoy rings relative to M is contained in the class of right McCoy rings, and we present an example of a u.p.-monoid M for which this containment is strict.
Mazurek, Ryszard, Ziembowski, Michał
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Algebra Colloquium, 2011
In this paper, we introduce power-serieswise McCoy rings, which are a generalization of power-serieswise Armendariz rings, and investigate their properties. We show that a ring R is power-serieswise McCoy if and only if the ring consisting of n × n upper triangular matrices with equal diagonal entries over R is power-serieswise McCoy.
Yang, Shizhou +2 more
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In this paper, we introduce power-serieswise McCoy rings, which are a generalization of power-serieswise Armendariz rings, and investigate their properties. We show that a ring R is power-serieswise McCoy if and only if the ring consisting of n × n upper triangular matrices with equal diagonal entries over R is power-serieswise McCoy.
Yang, Shizhou +2 more
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A note on complete rings of quotients and McCoy rings
Rendiconti del Circolo Matematico di Palermo, 2012Let \(R\) be a commutative ring with \(1 \neq 0\), total quotient ring \(\mathrm{tq}(R)\), complete ring of quotients \(C(R)\), and \(Z(R)\) its set of zero-divisors. Recall that \(R\) is a McCoy ring if ann\(_R(I) \neq 0\) for every finitely generated ideal \(I\) of \(R\) with \(I \subseteq Z(R)\). In [Rend. Circ. Mat. Palermo (2) 61, No. 1, 123--131 (
Dobbs, David E., Shapiro, Jay
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Nilpotent elements and McCoy rings
Studia Scientiarum Mathematicarum Hungarica, 2012We introduce the concept of nil-McCoy rings to study the structure of the set of nilpotent elements in McCoy rings. This notion extends the concepts of McCoy rings and nil-Armendariz rings. It is proved that every semicommutative ring is nil-McCoy. We shall give an example to show that nil-McCoy rings need not be semicommutative. Moreover, we show that
Liang Zhao, Xiaosheng Zhu, Qinqin Gu
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McCoy property of Hurwitz series rings
Asian-European Journal of Mathematics, 2020Based on a theorem of McCoy on commutative rings, Nielsen called a ring [Formula: see text] right McCoy if for any nonzero polynomials [Formula: see text] over [Formula: see text], [Formula: see text] implies [Formula: see text] for some [Formula: see text]. In this note, we introduce and investigate McCoy and [Formula: see text]-properties of Hurwitz
Vahid Nourozi +2 more
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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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