Results 121 to 130 of about 211 (141)

ARMENDARIZ RINGS AND SEMICOMMUTATIVE RINGS

Communications in Algebra, 2002
In 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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ON Π-NEAR-ARMENDARIZ RINGS

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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On constant Armendariz rings

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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On linearly weak Armendariz rings

Journal of Pure and Applied Algebra, 2015
An 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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Armendariz group rings

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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On skew Hurwitz serieswise Armendariz rings

Asian-European Journal of Mathematics, 2014
For a ring endomorphism α, we introduce and investigate skew Hurwitz serieswise Armendariz (or SHA) rings which are a generalization of α-rigid rings and determine the radicals of the skew Hurwitz series ring (HR, α), in terms of those of R. We prove that several properties transfer between R and the extensions, in case R is an SHA-ring.
Ahmadi, M., Moussavi, A., Nourozi, V.
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Quasi-central Armendariz rings

Journal of Algebra and Its Applications, 2020
A 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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On *-Skew *-Armendariz *-Rings

International Science and Technology Journal
A ring R is called α-*-skew *-Armendariz*-rings if whenever the polynomials p=∑_(i=0)^m▒〖a_i x^i 〗 and q=∑_(j=0)^n▒a_j x^j ∈ R[x,α] satisfy p(x)q(x) = p(x)q^* (x) = 0, then a_i α^j (b_j )= 0 for all i,j (consequently a_i α^j (b_j^* )= 0 ), which is a proper generalization of reduced*-rings.
Basma M. ELgamudi, Fatma A. Hamad
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π-Armendariz rings relative to a monoid

Frontiers of Mathematics in China, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Yao, Jiang, Meimei, Ren, Yanli
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Polynomial Rings Over Weak Armendariz Rings need not be Weak Armendariz

Communications in Algebra, 2014
It 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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