Results 21 to 30 of about 211 (141)

A KIND OF GRAPH STRUCTURE ASSOCIATED WITH ZERO-DIVISORS OF MONOID RINGS [PDF]

Journal of Algebraic Systems
Let $R$ be an associative ring and $M$ be a monoid‎. ‎In this paper‎, ‎we introduce new kind of graph structure asociated with zero-divisors of monoid ring $R[M]$‎, ‎calling it the $M$-Armendariz graph of a ring $R$ and denoted by $A(R,M)$‎.
Mohammad Etezadi, Abdollah Alhevaz
doaj   +1 more source

Extension of Antoine’s Ring Construction

International Journal of Mathematics and Mathematical Sciences, 2019
This article concerns a kind of extension of Antoine’s ring construction which is unit-IFP and Armendariz. Such extensions are also shown to be unit-IFP and Armendariz, by which we may extend the classes of unit-IFP and Armendariz rings.
Tai Keun Kwak
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Weak Armendariz Ideals

پژوهش‌های ریاضی, 2021
In this article, we introduce the weak Armendariz ideals as a generalization of the Armendariz ideals and we examine its properties, its relation to other structures.
Javad Nikmehr, Abdolreza Azadi
doaj  

On a theorem of McCoy [PDF]

Mathematica Bohemica
We study McCoy's theorem to the skew Hurwitz series ring $({\rm HR}, \omega)$ for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings.
Rajendra Kumar Sharma, Amit B. Singh
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The Armendariz module and its application to the Ikeda-Nakayama module

International Journal of Mathematics and Mathematical Sciences, 2006
A ring R is called a right Ikeda-Nakayama (for short IN-ring) if the left annihilator of the intersection of any two right ideals is the sum of the left annihilators, that is, if ℓ(I∩J)=ℓ(I)+ℓ(J) for all right ideals I and J of R. R is called Armendariz
M. Tamer Koşan
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Propiedad de Armendariz para las extensiones PBW torcidas y su anillo clásico de cocientes

Revista Integración, 2016
Consideramos un primer acercamiento a la noción de anillo de Armendariz para una extensión torcida de Poincaré-Birkho-Witt (PBW), y su anillo clásico de cocientes.
Armando Reyes, Héctor Suárez
doaj   +1 more source

A GENERALIZATION OF NIL-ARMENDARIZ RINGS

Journal of Algebra and Its Applications, 2013
Let R be a ring, M a monoid and ω : M → End (R) a monoid homomorphism. The skew monoid ring R * M is a common generalization of polynomial rings, skew polynomial rings, (skew) Laurent polynomial rings and monoid rings. In the current work, we study the nil skew M-Armendariz condition on R, a generalization of the standard nil-Armendariz condition from
Habibi, Mohammad, Manaviyat, Raoufeh
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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  

Properties of Armendariz rings and weak Armendariz rings

Publications de l'Institut Mathematique, 2009
We consider some properties of Armendariz and rigid rings. We prove that the direct product of rigid (weak rigid), weak Armendariz rings is a rigid (weak rigid), weak Armendariz ring. On the assumption that the factor ring R/I is weak Armendariz, where I is nilpotent ideal, we prove that R is a weak Armendariz ring.
openaire   +3 more sources

On Nil-Symmetric Rings

Journal of Mathematics, 2014
The concept of nil-symmetric rings has been introduced as a generalization of symmetric rings and a particular case of nil-semicommutative rings. A ring R is called right (left) nil-symmetric if, for a,b,c∈R, where a,b are nilpotent elements, abc=0  (cab=
Uday Shankar Chakraborty, Krishnendu Das
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