Results 1 to 10 of about 306 (165)
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 Related Concepts [PDF]
مجلة بغداد للعلوم, 2016 In this paper we investigated some new properties of ?-Armendariz rings and studied the relationships between ?-Armendariz rings and central Armendariz rings, nil-Armendariz rings, semicommutative rings, skew Armendariz rings, ?-compatible rings and ...
Baghdad Science Journal
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Nilpotent elements and Armendariz rings [PDF]
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 [PDF]
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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Classifications of Several Classes of Armendariz-like Rings Relative to an Abelian Monoid and Its Applications [PDF]
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, Yajun Ma
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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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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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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
Yang Lee
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Communications in Algebra, 2004 Abstract A ring R is called Armendariz if, whenever in R[x], a i b j = 0 for all i and j. In this paper, some “relatively maximal” Armendariz subrings of matrix rings are identified, and a necessary and sufficient condition for a trivial extension to be Armendariz is obtained. Consequently, new families of Armendariz rings are presented.
Tsiu-Kwen Lee, Yiqiang Zhou
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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
openaire +2 more sources