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QUASI-ARMENDARIZ PROPERTY FOR SKEW POLYNOMIAL RINGS

, 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, Baser, Muhittin, Kwak, Tai Keun, Tai Keun Kwa   +3 more
core   +1 more source

A NOTE ON QUASI-ARMENDARIZ RINGS A NOTE ON QUASI-ARMENDARIZ RINGS A NOTE ON QUASI-ARMENDARIZ RINGS

, 2020
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.
Zhang Wenhui, Liu Zhongkui
core  

Semicommutative and Armendariz Matrix Rings

In this paper, we construct some interesting high-order upper triangular matrix rings, which have semicommutative and Armendariz properties.
Gang Yang
core   +1 more source

Nilpotent elements and Armendariz rings [PDF]

Journal of Algebra, 2008
We study the structure of the set of nilpotent elements in Armendariz rings and introduce nil-Armendariz as a generalization. We also provide some new examples by proving that if D is a K-algebra and n⩾2, the coproduct D∗KK〈x|xn=0〉 is Armendariz if and ...
Ramon Antoine
exaly   +2 more sources

ON JACOBSON AND NIL RADICALS RELATED TO POLYNOMIAL RINGS

Journal of the Korean Mathematical Society, 2016
This note is concerned with examining nilradicals and Jacobson radicals of polynomial rings when related factor rings are Armendariz. Especially we elaborate upon a well-known structural property of Armendariz rings, bringing into focus the Armendariz ...
Tai Keun Kwak, Yang Lee, A Cigdem Ozcan
exaly   +2 more sources

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Nilpotent elements and nil-Armendariz property of skew generalized power series rings

Asian-European Journal of Mathematics, 2016
Let [Formula: see text] be a ring, [Formula: see text] a strictly ordered monoid, and [Formula: see text] a monoid homomorphism. The skew generalized power series ring [Formula: see text] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal’cev–Neumann Laurent ...
Paykan, Kamal, Moussavi, Ahmad
openaire   +1 more source

Nil-Armendariz Rings Relative to a Monoid

Mediterranean Journal of Mathematics, 2012
Ebrahim Hashemi
exaly   +2 more sources