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Semicommutative and Armendariz Matrix Rings

Axioms
In this paper, we construct some interesting high-order upper triangular matrix rings, which have semicommutative and Armendariz properties. Also, the relatively maximality of these rings as subrings of certain matrix rings is considered.
Gang Yang
doaj   +4 more sources

On weakened $(\alpha,\delta)$-skew Armendariz rings [PDF]

Mathematica Bohemica, 2022
In this note, for a ring endomorphism $\alpha$ and an $\alpha$-derivation $\delta$ of a ring $R$, the notion of weakened $(\alpha,\delta)$-skew Armendariz rings is introduced as a generalization of $\alpha$-rigid rings and weak Armendariz rings.
Alireza Majdabadi Farahani, Mohammad Maghasedi, Farideh Heydari, Hamidagha Tavallaee   +3 more
doaj   +2 more sources

Weak Quasi-Armendariz Rings [PDF]

Algebra Colloquium, 2011
In this paper, we introduce and study weak quasi-Armendariz rings which unify the notions of weak Armendariz rings and quasi-Armendariz rings. It is shown that the weak quasi-Armendarizness is a Morita invariant property. For a semiprime ring R, it is shown that R[x]/〈xn〉 is weak quasi-Armendariz, where R[x] is the polynomial ring over R and 〈xn〉 is ...
Baser, Muhittin, Kaynarca, Fatma, Kwak, Tai Keun, Lee, Yang   +3 more
core   +8 more sources

?-Armendariz Rings and Related Concepts [PDF]

مجلة بغداد للعلوم, 2016
In this paper we investigated some new properties of ?-Armendariz rings and studied the relationships between ?-Armendariz rings and central Armendariz rings, nil-Armendariz rings, semicommutative rings, skew Armendariz rings, ?-compatible rings and ...
Baghdad Science Journal
doaj   +2 more sources

Central Armendariz rings. [PDF]

, 2011
Let \(R\) be a ring with 1, \(C\) the center of \(R\), \(R[x]\) the polynomial ring with an indeterminate \(x\), and \(R[x,x^{-1}]\) the Laurent polynomial ring. If \((\sum_{i=0}^n a_ix^i)(\sum_{j=0}^m b_jx^j)=0\) for \(\sum_{i=0}^n a_ix^i,\sum_{j=0}^m b_jx^j\not=0\) in \(R[x]\) implies that \(a_ib_j\in C\) for all \(i\) and \(j\), then \(R\) is called
HALICIOĞLU, SAİT, Harmanci, Abdullah, Gungoroglu, Gonca, Agayev, Nazim   +3 more
core   +5 more sources

Classifications of Several Classes of Armendariz-like Rings Relative to an Abelian Monoid and Its Applications

Mathematics
Let M be an Abelian monoid. A necessary and sufficient condition for the class ArmM of all Armendariz rings relative to M to coincide with the class Arm of all Armendariz rings is given.
Jianwei He, Yajun Ma
doaj   +3 more sources

ON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS [PDF]

Journal of Algebraic Systems, 2015
Let $alpha$ be an automorphism of a ring $R$. The authors [On skewinverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1)(2012) 138-156] applied the concept of Armendariz rings to inverseskew Laurent series rings and introduced skew ...
Mohammad Habibi
doaj   +3 more sources

On Classical Quotient Rings of Skew Armendariz Rings [PDF]

International Journal of Mathematics and Mathematical Sciences, 2007
Let R be a ring, α an automorphism, and δ an α-derivation of R. If the classical quotient ring Q of R exists, then R is weak α-skew Armendariz if and only if Q is weak α˜-skew Armendariz.
A. R. Nasr-Isfahani, A. Moussavi
doaj   +3 more sources

Extended Armendariz Rings [PDF]

, 2013
In this note we introduce central linear Armendariz rings as a generalization of Armendariz rings and investigate their properties.
Agayev, Nazım, Harmancı, Abdullah, Halıcıoğlu, Sait   +2 more
openaire   +4 more sources

Skew Polynomial Extensions over Zip Rings [PDF]

International Journal of Mathematics and Mathematical Sciences, 2008
In this article, we study the relationship between left (right) zip property of 𝑅 and skew polynomial extension over 𝑅, using the skew versions of Armendariz rings.
Wagner Cortes
doaj   +3 more sources