Results 1 to 10 of about 192 (123)
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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The Armendariz Graph of a Ring
Discussiones Mathematicae - General Algebra and Applications, 2018 In this paper we initiate the study of Armendariz graph of a commutative ring R and investigate the basic properties of this graph such as diameter, girth, domination number, etc.
Abdioğlu Cihat +2 more
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ON A RING PROPERTY GENERALIZING POWER-ARMENDARIZ AND CENTRAL ARMENDARIZ RINGS
Korean Journal of Mathematics, 2015 Summary: We in this note consider a class of rings which is related to both power-Armendariz and central Armendariz rings, in the spirit of Armendariz and Kaplansky. We introduce central power-Armendariz as a generalization of them, and study the structure of central products of coefficients of zero-dividing polynomials.
Sung Ju Ryu, Sang Jo Yun, Yeonsook Seo
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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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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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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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?-Armendariz Rings and Related Concepts
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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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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A PROOF ON POWER-ARMENDARIZ RINGS
Korean Journal of Mathematics, 2013 Summary: Power-Armendariz is a unifying concept of Armendariz and commutative. Let \(R\) be a ring and \(I\) be a proper ideal of \(R\) such that \(R/I\) is a power-Armendariz ring. Han et al. proved that if \(I\) is a reduced ring without identity then \(R\) is power-Armendariz.
Sung Ju Ryu, Yeonsook Seo
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