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A randomized clinical trial of app cognitive behavior therapy vs. HealthWatch for obsessive compulsive disorder. [PDF]
Wilhelm S +9 more
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The McCoy Condition on Skew Polynomial Rings
Based 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.
Muhittin Baser +2 more
exaly +4 more sources
The McCoy Condition on Noncommutative Rings
McCoy 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
Chan Yong Hong, , Yang Lee
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Extensions of Rings Having McCoy Condition
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
Kosan, MUHAMMET TAMER
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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 ...
A Moussavi, Abdollah 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 ...
Abdollah Alhevaz, A Moussavi
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