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Semi-commutativity and the McCoy condition
Journal of Algebra, 2006 A ring \(R\) is called `right McCoy' if it satisfies: whenever \(f(x)g(x)=0\) in \(R[X]\) for non-zero polynomials \(f(x)\) and \(g(x)\), then there is a non-zero \(r\in R\) with \(f(x)r=0\). \(R\) is called a `McCoy ring' if it is both left and right McCoy. It is known that any commutative ring and any reduced ring is a McCoy ring.
Pace P. Nielsen
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MCCOY CONDITION ON IDEALS OF COEFFICIENTS [PDF]
Bulletin of the Korean Mathematical Society, 2013 We continue the study of McCoy condition to analyze zero- dividing polynomials for the constant annihilators in the ideals generated by the coefficients. In the process we introduce the concept ofideal- - McCoy rings, extending known results related to McCoy condition. It is shown that the class of ideal- -McCoy rings contains both strongly McCoy rings
Jeoung Soo Cheon +3 more
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ON A GENERALIZATION OF THE MCCOY CONDITION [PDF]
Journal of the Korean Mathematical Society, 2010 We in this note consider a new concept, so called …-McCoy, which unifies McCoy rings and IFP rings. The classes of McCoy rings and IFP rings do not contain full matrix rings and upper (lower) triangular matrix rings, but the class of …-McCoy rings contain upper (lower) trian- gular matrix rings and many kinds of full matrix rings.
Young-Cheol Jeon +5 more
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Extensions of Rings Having McCoy Condition [PDF]
Canadian Mathematical Bulletin, 2009 AbstractLet 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
M. Tamer Koşan
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Some New Classes of Rings Which Have the McCoy Condition [PDF]
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Danchev, Peter, Zahiri, M.
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On a McCoy-like condition for rings [PDF]
We study rings $R$ for which whenever non-zero polynomials $f(x)$ and $g(x)$ satisfy $f(x)g(x)f(x)=0$, it implies that there is a non-zero element $r\in R$ such that $f(x)rf(x)=0$. We call such rings inner McCoy rings. We explore some examples of rings that are inner McCoy, determine relationships between the class of inner McCoy rings and some known ...
Thimmaiah, Sharang, DSouza, Raisa
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On modules related to McCoy modules
Open Mathematics, 2022 In this paper, we first investigate the relationships between the McCoy module and related modules based on their relationships in rings. After that, we improve some properties of McCoy modules and introduce ZPZC modules which extend the notion of McCoy ...
Baeck Jongwook
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Composite Hurwitz Rings as PF-Rings and PP-Rings
Mathematics, 2020 Let R ⊆ T be an extension of commutative rings with identity and H ( R , T ) (respectively, h ( R , T ) ) the composite Hurwitz series ring (respectively, composite Hurwitz polynomial ring).
Dong Kyu Kim, Jung Wook Lim
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BMC Anesthesiology, 2020 Background Immobilization with cervical spine worsens endotracheal intubation condition. Though various intubation devices have been demonstrated to perform well in oral endotracheal intubation, limited information is available concerning nasotracheal ...
Kwon Hui Seo +5 more
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