Results 141 to 150 of about 300,701 (162)
QUASI-ARMENDARIZ PROPERTY FOR SKEW POLYNOMIAL RINGS
Communications of the Korean Mathematical Society, 2011 The concept of the quasi-Armendariz property of rings properly contains Armendariz rings and semiprime rings. In this paper, we extend the quasi-Armendariz property for a polynomial ring to the skew polynomial ring, hence we call such ring a sigma-quasi ...
Muhittin Baser
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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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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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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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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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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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Communications in Algebra, 2016
ABSTRACTFor a torsion or torsion-free group G and a field F, we characterize the group algebra FG that is Armendariz. Armendariz property for a group ring over a general ring R is also studied and related to those of Abelian group rings and the quaternion ring over R.
Liu Yang, Xiankun Du
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ABSTRACTFor a torsion or torsion-free group G and a field F, we characterize the group algebra FG that is Armendariz. Armendariz property for a group ring over a general ring R is also studied and related to those of Abelian group rings and the quaternion ring over R.
Liu Yang, Xiankun Du
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$\mathcal {Z}$-Armendariz Rings and Modules
Vietnam Journal of Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nejadzadeh, Afsaneh +3 more
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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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Quasi-central Armendariz rings
Journal of Algebra and Its Applications, 2020A ring [Formula: see text] is said to be quasi-central Armendariz if [Formula: see text] and [Formula: see text] satisfy [Formula: see text] then [Formula: see text] for all [Formula: see text] and [Formula: see text]. It is proved that if [Formula: see text] is a quasi-central Armendariz ring then [Formula: see text] implies that all [Formula: see ...
Liu, Yufeng, Chen, Weixing
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