Results 61 to 70 of about 179 (118)

A Study of Generalized Differential Identities via Prime Ideals

Journal of Mathematics, Volume 2025, Issue 1, 2025.
Let R be a ring and P be a prime ideal of R. The aim of this research paper is to delve into the relationship between the structural properties of the quotient ring R/P and the behavior of generalized derivations in a ring R endowed with an involution.
Ali Yahya Hummdi, Kamal Charrabi, Shakir Ali, Abdellah Mamouni, Faranak Farshadifar   +4 more
wiley   +1 more source

A Commutativity theorem for semiprime rings [PDF]

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1980
AbstractIt is shown that if R is a semiprime ring with 1 satisfying the property that, for each x, y ∈ R, there exists a positive integer n depending on x and y such that (xy)k − xkyk is central for k = n,n+1, n+2, then R is commutative, thus generalizing a result of Kaya.
openaire   +2 more sources

On semiprime segments of rings [PDF]

Journal of the Australian Mathematical Society, 2006
AbstractA semiprime segment of a ring R is a pair P2 ⊂ P1 of semiprime ideals of R such that ∩ In ⊆ P2 for all ideals I of R with P2 ⊂ I ⊂ P1. In this paper semiprime segments with P1 a comparizer ideal are classified as either simple, exceptional, or archimedean, extending to several classes of rings a classification known for right chain rings. These
Mazurek, R., Törner, G.
openaire   +2 more sources

Modules With Epimorphisms Between Their Submodules

Journal of Mathematics, Volume 2025, Issue 1, 2025.
An R‐module M is called weakly uniserial if its submodules are comparable regarding embedding, i.e., if for any two submodules N, K of M, HomR(N, K) or HomR(K, N) contains an injective element. Here, we are interested in studying modules which for any two submodules of them there is an epimorphism from one to the other.
P. Karimi Beiranvand, Pramita Mishra
wiley   +1 more source

Higher Derivations Satisfying Certain Identities in Rings

Journal of Mathematics, Volume 2024, Issue 1, 2024.
Let n and m be fixed positive integers. In this paper, we establish some structural properties of prime rings equipped with higher derivations. Motivated by the works of Herstein and Bell‐Daif, we characterize rings with higher derivations D=dii∈N satisfying (i) dnx,dmy∈ZR for all x,y∈R and (ii) dnx,y∈ZR for all x,y∈R.
Amal S. Alali, Shakir Ali, Naira N. Rafiquee, Vaishali Varshney, Faranak Farshadifar   +4 more
wiley   +1 more source

A SUBCLASS OF BAER IDEALS AND ITS APPLICATIONS [PDF]

Journal of Algebraic Systems
An ideal $I$ of a ring $R$ is called a right strongly Baer ideal if $r(I)=r(e)$, where $e$ is an idempotent, and there are right semicentral idempotents $e_{i}$ ($1\leq i\leq n$) with $ReR=Re_{1}R\cap Re_{2}R\cap...\cap Re_{n}R$ and each ideal $Re_{i}R ...
Zainab Gharabagi, Ali Taherifar
doaj   +1 more source

On Fully Semiprime Submodules and Fully Semiprime Modules

Ibn Al-Haitham Journal for Pure and Applied Sciences, 2017
   Let R be a commutative ring with unity and let M be a unitary R-module. In this paper we study fully semiprime submodules and fully semiprime modules, where a proper fully invariant R-submodule W of M is called fully semiprime in M if whenever Xï ...
I.M.A. Hadi, B.N. Shihab
doaj  

Left centralizers on rings that are not semiprime

Rocky Mountain Journal of Mathematics, 2011
In any ring \(R\), an additive \(T\colon R\to R\) is a (left) centralizer on \(R\) if \(T(xy)=T(x)y\) for all \(x,y\in R\), and is a Jordan centralizer when \(T(xy+yx)=T(x)y+T(y)x\). The main result of the paper is that for any Jordan centralizer \(T\) of \(R\), if \(I\) is the \(T\)-invariant ideal of \(R\) generated by \(\{T(xy)-T(x)y\mid x,y\in R\}\)
Hentzel, Irvin, El-Sayiad, M.S.
openaire   +3 more sources

A remark on centralizers in semiprime rings

Glasnik matematički, 2004
The purpose of this paper is to prove the following result: Let m 1, n 1 be fixed integers and let R be a (m + n + 2)!-torsion free semiprime ring with the identity element. Suppose there exists an additive mapping T : R R, such that T(xm+n+1) = xm T(x) xn holds for all x R. In this case T is a centralizer.
openaire   +3 more sources

Identities with derivations and automorphisms on semiprime rings

International Journal of Mathematics and Mathematical Sciences, 2005
The purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative ...
Joso Vukman
doaj   +1 more source