Results 91 to 100 of about 113,306 (118)
The McCoy Condition on Ore Extensions
Communications in Algebra, 2013 Nielsen [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
exaly +4 more sources
The McCoy Condition on Skew Polynomial Rings
Communications in Algebra, 2009 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 Başer, Tai Keun Kwak, Yang Lee
exaly +4 more sources
Zero-divisor placement, a condition of Camillo, and the McCoy property
Journal of Pure and Applied Algebra, 2020 Let \(R\) 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
openaire +3 more sources
The McCoy Condition on Noncommutative Rings
Communications in Algebra, 2011 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 +3 more
openaire +2 more sources
The McCoy condition on skew monoid rings
Asian-European Journal of Mathematics, 2017 Let [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
openaire +3 more sources
The McCoy Condition on Skew Poincaré–Birkhoff–Witt Extensions
Communications in Mathematics and Statistics, 2019 Let \(B\) 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
openaire +2 more sources
Some of the next articles are maybe not open access.
Related searches:
Related searches:
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
openaire +3 more sources