Results 141 to 150 of about 306 (165)
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Communications in Algebra, 2010
We construct various examples of Armendariz and related rings by reviewing and extending some results concerning the structure of nil(R). In particular, we give some examples of Armendariz rings related to power series rings and an example of an n-Armendariz ring, for all n ≥ 1, which is not Armendariz.
Ramon Antoine
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We construct various examples of Armendariz and related rings by reviewing and extending some results concerning the structure of nil(R). In particular, we give some examples of Armendariz rings related to power series rings and an example of an n-Armendariz ring, for all n ≥ 1, which is not Armendariz.
Ramon Antoine
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Polynomial Rings Over Weak Armendariz Rings need not be Weak Armendariz
Communications in Algebra, 2014It is proved that there exists a weak Armendriz ring R over which the polynomial ring R[x] is not weak Armendariz. This answers an open question of Liu and Zhao in 2006 in the negative, and eliminates the misunderstanding of the question having a positive solution by Hashemi in 2008.
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A NOTE ON QUASI-ARMENDARIZ RINGS [PDF]
Mathematical Journal of Okayama University, 2010 A ring R is called a quasi-Armendariz ring if whenever elements α = a 0 +a 1 x+a 2 x 2 +· · ·+a n x n , β = b 0 +b 1 x+b 2 x 2 +· · ·+b m x m ∈ R[x] satisfy αR[x]β = 0, then a i Rb j = 0 for each i, j. In this note we consider quasi-Armendariz property of a special subring of the infinite upper triangular matrix ring over a ring R.
Zhongkui, Liu, Wenhui, Zhang
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Asian-European Journal of Mathematics, 2012
Antoine [Nilpotent elements and Armendariz rings, J. Algebra319 (2008) 3128–3140] studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. When the set of nilpotent elements of a ring R with an α-condition, namely α-compatibility, forms an ideal, we observe that R satisfies a nil Armendariz-type ...
Habibi, M., Moussavi, A.
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Antoine [Nilpotent elements and Armendariz rings, J. Algebra319 (2008) 3128–3140] studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. When the set of nilpotent elements of a ring R with an α-condition, namely α-compatibility, forms an ideal, we observe that R satisfies a nil Armendariz-type ...
Habibi, M., Moussavi, A.
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Generalizations of reversible and Armendariz rings
International Journal of Algebra and Computation, 2016This paper concerns several ring theoretic properties related to matrices and polynomials. The basic properties of [Formula: see text]-reversible and power-Armendariz are studied. We provide a method by which one can always construct a power-Armendariz ring but neither symmetric nor Armendariz from given any symmetric ring. We investigate next various
Juncheol Han +4 more
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Extensions of Generalized Armendariz Rings
Algebra Colloquium, 2006A ring R is called Armendariz if whenever the product of any two polynomials in R[x] over R is zero, then so is the product of any pair of coefficients from the two polynomials. Such rings have been extensively studied in literature. For a ring endomorphism α, we introduce the notion of α-Armendariz rings by considering the polynomials in the skew ...
Hong, Chan Yong +2 more
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ARMENDARIZ RINGS AND SEMICOMMUTATIVE RINGS
Communications in Algebra, 2002In this note we concern the structures of Armendariz rings and semicommutative rings which are generalizations of reduced rings, the classical right quotient rings of Armendariz rings, the polynomi...
Chan Huh, Yang Lee, Agata Smoktunowicz
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Asian-European Journal of Mathematics, 2009
In this note we introduce a concept, so-called π-Near-Armendariz ring, that is a generalization of both Armendariz rings and 2-primal rings. We first observe the basic properties of π-Near-Armendariz rings, constructing typical examples. We next extend the class of π-Near-Armendariz rings, through various ring extensions.
Ghalandarzadeh, Sh., Malakooti Rad, P.
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In this note we introduce a concept, so-called π-Near-Armendariz ring, that is a generalization of both Armendariz rings and 2-primal rings. We first observe the basic properties of π-Near-Armendariz rings, constructing typical examples. We next extend the class of π-Near-Armendariz rings, through various ring extensions.
Ghalandarzadeh, Sh., Malakooti Rad, P.
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Asian-European Journal of Mathematics, 2016
Let [Formula: see text] be a ring equipped with an endomorphism [Formula: see text] and an [Formula: see text]-derivation [Formula: see text]. In this article, we study [Formula: see text]-constant Armendariz rings and radicals of the Ore extension [Formula: see text], in terms of a [Formula: see text]-constant Armendariz ring [Formula: see text] with
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Let [Formula: see text] be a ring equipped with an endomorphism [Formula: see text] and an [Formula: see text]-derivation [Formula: see text]. In this article, we study [Formula: see text]-constant Armendariz rings and radicals of the Ore extension [Formula: see text], in terms of a [Formula: see text]-constant Armendariz ring [Formula: see text] with
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On linearly weak Armendariz rings
Journal of Pure and Applied Algebra, 2015An associative ring \(R\) with identity is called linearly weak Armendariz if for all \(f(x)=a_0+a_1x,\;g(x)=b_0+b_1x\in R[x]\) such that \(f(x)g(x)=0\) we have \(a_ib_j\) is nilpotent for all \(i,j\). In this paper, properties of linearly weak Armendariz rings are studied.
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