Results 121 to 130 of about 221 (141)

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 Armendariz Rings

Communications in Algebra, 2003
Abstract For a ring endomorphism α, we introduce α-skew Armendariz rings which are a generalization of α-rigid rings and Armendariz rings, and investigate their properties. Moreover, we study on the relationship between the Baerness and p.p.-property of a ring R and these of the skew polynomial ring R[x; α] in case R is α-skew Armendariz.
Chan Yong Hong, Nam Kyun Kim, Tai Keun Kwak   +2 more
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$\mathcal {Z}$-Armendariz Rings and Modules

Vietnam Journal of Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nejadzadeh, Afsaneh, Amini, Afshin, Amini, Babak, Sharif, Habib   +3 more
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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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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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Examples of Armendariz Rings

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.
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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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A NOTE ON SKEW ARMENDARIZ RINGS

Communications in Algebra, 2005
ABSTRACT In this note,we answer a question of Hong et al. (2003) by proving that if α is a monomorphism of a reduced ring R, and R is α-skew Armendariz, then R is α-rigid.
Weixing Chen, Wenting Tong
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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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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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