Results 71 to 80 of about 852 (157)
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 +4 more
wiley +1 more source
Jordan ?-Centralizers of Prime and Semiprime Rings
مجلة بغداد للعلوم, 2010 The purpose of this paper is to prove the following result: Let R be a 2-torsion free ring and T: R?R an additive mapping such that T is left (right) Jordan ?-centralizers on R.
Baghdad Science Journal
doaj +1 more source
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
COMMUTING AND 2-COMMUTING DERIVATIONS OF SEMIPRIME RINGS
Journal of Kufa for Mathematics and Computer, 2012 The main purpose of this paper is to study and investigate some results concerning generalized derivation D on semiprime ring R, we obtain a derivation d is commuting and 2-commuting on R.
Mehsin Jabel Atteya +1 more
doaj +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 +4 more
wiley +1 more source
Derivations of higher order in semiprime rings
International Journal of Mathematics and Mathematical Sciences, 1998 Let R be a 2-torsion free semiprime ring with derivation d. Supposed d2n is a derivation of R, where n is a positive integer. It is shown that if R is (4n−2)-torsion free or if R is an inner derivation of R, then d2n−1=0.
Jiang Luh, Youpei Ye
doaj +1 more source
On Additivity and Multiplicativity of Centrally Extended (α, β)‐Higher Derivations in Rings
International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.In this paper, the concept of centrally extended (α, β)‐higher derivations is studied. It is shown to be additive in a ring without nonzero central ideals. Also, we prove that in semiprime rings with no nonzero central ideals, every centrally extended (α, β)‐higher derivation is an (α, β)‐higher derivation.
O. H. Ezzat, Attila Gil nyi
wiley +1 more source
The Baer Radical of Rings in Term of Prime and Semiprime Generalized Bi-ideals
, 2011 Using the idea of prime and semiprime bi-ideals of rings, the concept of prime and semiprime generalized bi-ideals of rings is introduced, which is an extension of the concept of prime and semiprime bi-ideals of rings and some interesting ...
Rattiya Boonruang, Aiyared Iampan
core +1 more source
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
SOME RESULTS IN SEMIPRIME RINGS WITH DERIVATION
, 2013 Let R be a semiprime ring and S be a nonempty subset of R. A mapping F from R to R is called centralizing on S if [F(x), x] is an element of Z for all x is an element of S. The mapping F is called strong commutativity preserving (SCP) on S if [F(x), F (y)
Koc, Emine
core +1 more source