Results 11 to 20 of about 306 (165)
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 +3 more
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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
Agayev, Nazım +3 more
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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
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 +2 more
openaire +5 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 +5 more sources
Nilpotent Elements in Skew Polynomial Rings [PDF]
Journal of Sciences, Islamic Republic of Iran, 2017 Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings.
M. Azimi, A. Moussavi
doaj +2 more sources
Quasi-Armendariz rings relative to a monoid [PDF]
Journal of Pure and Applied Algebra, 2007 Let \(M\) be a monoid. An associative ring \(R\) with an identity is called \(M\)-quasi-Armendariz if for any two elements \(a=a_1g_1+\cdots+a_ng_n\) and \(b=b_1h_1+\cdots+b_kh_k\), \(a_i,b_j\in R\), \(g_i,h_j\in M\), of the semigroup ring \(R[M]\) such that \(aR[M]b=0\) it follows that \(a_iRb_j=0\) for all \(i,j\).
Hashemi, Ebrahim
openaire +3 more sources
On Nilpotent Elements of Skew Polynomial Rings [PDF]
Journal of Mathematical Extension, 2012 We study the structure of the set of nilpotent elements in skew polynomial ring R[x; α], when R is an α-Armendariz ring. We prove that if R is a nil α-Armendariz ring and α t = IR, then the set of nilpotent elements of R is an α-compatible subrng of ...
J. Esmaeili, E. Hashemi
doaj +1 more source
Endo-Noetherian Skew Generalized Power Series Rings [PDF]
Assiut University Journal of Multidisciplinary Scientific Research, 2023 Endo-Noetherian modules were introduced by A. Kaidi and E. Sanchez] as a generalization of Noetherian modules. A left Ɍ-module M which satisfies the ascending chain condition for endomorphic kernels is said to be endo-Noetherian.
Ramy Abdel-Khaleq +2 more
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