Results 1 to 10 of about 143 (120)
On Classical Quotient Rings of Skew Armendariz Rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2007 Let R be a ring, α an automorphism, and δ an α-derivation of R. If the classical quotient ring Q of R exists, then R is weak α-skew Armendariz if and only if Q is weak α˜-skew Armendariz.
A. R. Nasr-Isfahani, A. Moussavi
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Armendariz Rings and Reduced Rings
Journal of Algebra, 2000 According to \textit{D. D. Anderson} and \textit{V. Camillo} [Commun. Algebra 26, No. 7, 2265-2272 (1998; Zbl 0915.13001)], a ring \(R\) is called Armendariz if whenever polynomials \(f(x)=a_0+a_1x+\cdots+a_m x^m\) and \(g(x)=b_0+b_1x+\cdots+b_nx^n\) in \(R[x]\) satisfy \(f(x)g(x)=0\), then \(a_ib_j=0\) for each \(i\), \(j\). It is shown that if a ring
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Nilpotent elements and Armendariz rings
Journal of Algebra, 2008 Let \(R\) denote an associative ring with \(1\), and let \(\text{nil}(R)\) denote the set of nilpotent elements. Further, let \(f(x)=\sum_{i=0}^ma_ix^i,g(x)=\sum_{j=0}^nb_jx^j\in R[x]\) denote two arbitrary polynomials. One says that \(R\) is an Armendariz ring if \(f(x)g(x)=0\) implies that \(a_ib_j=0\) for all \(i\) and \(j\).
Ramon Antoine
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Semicommutative and Armendariz Matrix Rings
AxiomsIn this paper, we construct some interesting high-order upper triangular matrix rings, which have semicommutative and Armendariz properties. Also, the relatively maximality of these rings as subrings of certain matrix rings is considered.
Gang Yang
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ON WEAK ARMENDARIZ RINGS [PDF]
Bulletin of the Korean Mathematical Society, 2009 In the present note we study the properties of weak Armen- dariz rings, and the connections among weak Armendariz rings, Armen- dariz rings, reduced rings and IFP rings. We prove that a right Ore ring R is weak Armendariz if and only if so is Q, where Q is the classical right quotient ring of R. With the help of this result we can show that a semiprime
Young-Cheol Jeon +3 more
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MathematicsLet M be an Abelian monoid. A necessary and sufficient condition for the class ArmM of all Armendariz rings relative to M to coincide with the class Arm of all Armendariz rings is given.
Jianwei He
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RINGS OVER WHICH POLYNOMIAL RINGS ARE ARMENDARIZ AND REVERSIBLE
Korean Journal of Mathematics, 2012 Summary: A ring \(R\) is called \textit{reversibly Armendariz} if \(b_j a_i = 0\) for all \(i,j\) whenever \(f(x)g(x) = 0\) for two polynomials \(f(x) = \sum_{i=0}^m {a_i x_i}\), \(g(x) = \sum_{j=0}^n {b_j x_j}\) over \(R\). It is proved that a ring \(R\) is reversibly Armendariz if and only if its polynomial ring is reversibly Armendariz if and only ...
Ahn, Jung Ho +12 more
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On weakened $(\alpha,\delta)$-skew Armendariz rings [PDF]
Mathematica Bohemica, 2022 In this note, for a ring endomorphism $\alpha$ and an $\alpha$-derivation $\delta$ of a ring $R$, the notion of weakened $(\alpha,\delta)$-skew Armendariz rings is introduced as a generalization of $\alpha$-rigid rings and weak Armendariz rings.
Alireza Majdabadi Farahani +3 more
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On Almost Armendariz Ring [PDF]
Algebra Colloquium, 2020 In this paper, we introduce the notion of an almost Armendariz ring, which is a generalization of an Armendariz ring, and discuss some of its properties. It has been found that every almost Armendariz ring is weak Armendariz but the converse is not true. We prove that a ring R is almost Armendariz if and only if R[x] is almost Armendariz.
Om Prakash, Sushma Singh, K.P. Shum
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