Results 41 to 50 of about 1,309,327 (169)

Commutativity results for semiprime rings with derivations

International Journal of Mathematics and Mathematical Sciences, 1998
We extend a result of Herstein concerning a derivation d on a prime ring R satisfying [d(x),d(y)]=0 for all x,y∈R, to the case of semiprime rings. An extension of this result is proved for a two-sided ideal but is shown to be not true for a one-sided ...
Mohammad Nagy Daif
doaj   +1 more source

On Prime and Semiprime Gamma Rings with Symmetric Gamma n-Centralizers

, 2021
In this paper, we assume that M is Γ-ring then we will present the definition of symmetric Γ-n-centralizers and the definition of Jordan Γ-n-centralizers of M.
Ikram A. Saed
semanticscholar   +1 more source

Regular elements in semiprime rings [PDF]

Proceedings of the American Mathematical Society, 1968
In the proof of Goldie's theorem [1, Theorem 4.1], one of the crucial steps is to establish that every large right ideal contains a regular element [1, Theorem 3.9]. Recently, S. A. Amitsur told one of the authors he had proved, using the weaker conditions of the ACC on left and right annihilators, that every prime ring contains a left regular element ...
Johnson, R. E., Levy, L. S.
openaire   +2 more sources

A note on a pair of derivations of semiprime rings

International Journal of Mathematics and Mathematical Sciences, 2004
We study certain properties of derivations on semiprime rings. The main purpose is to prove the following result: let R be a semiprime ring with center Z(R), and let f, g be derivations of R such that f(x)x+xg(x)∈Z(R) for all x∈R, then f and g are ...
Muhammad Anwar Chaudhry, A. B. Thaheem
doaj   +1 more source

Some Results on Reduced Rings

مجلة بغداد للعلوم, 2008
The main purpose of this paper is to study some results concerning reduced ring with another concepts as semiprime ring ,prime ring,essential ideal ,derivations and homomorphism ,we give some results a bout that.
Baghdad Science Journal
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$\Gamma^*$-DERIVATION ACTING AS AN ENDOMORPHISM AND AS AN ANTI-ENDOMORPHISM IN SEMIPRIME $\Gamma$-RING M WITH INVOLUTION

, 2015
Let M be a semiprime -ring with involution satisfying the con- dition that abc = abc (a, b, c ∈ M and , ∈ ). An additive mapping d : M → M is called -derivation if d(xy) = d(x) y +xd(y).
A. Kadhim, Hajar Sulaiman, A. Majeed
semanticscholar   +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

On S-Prime and S-Semiprime RΓ-Submodules of RΓ-Module

, 2021
Let R be a Γ-ring and G be a RΓ-module. Aproper RΓ-submodule E of G is said to be S-prime (S-semiprime) RΓ-submodule of G whenever μ(K) ⊆ E ( μ(m) γ μ(m) E ), for some K be a RΓ-submodule of G, where End (G), y Γ and m G, then K ⊆ E or M(G)⊆ E ( μ(m) E).
Ali Abd Alhussein Zyarah, N. Al-Mothafar
semanticscholar   +1 more source

Semiprime SF-rings whose essential left ideals are two-sided

International Journal of Mathematics and Mathematical Sciences, 1994
It is proved that if R is a semiprime ELT-ring and every simple right R-module is flat then R is regular. Is R regular if R is a semiprime ELT-ring and every simple right R-module is flat? In this note, we give a positive answer to the question.
Zhang Jule, Du Xhianneng
doaj   +1 more source

Orthogonal Symmetric Higher bi-Derivations on Semiprime Г-Rings

مجلة بغداد للعلوم, 2019
Let M is a Г-ring. In this paper the concept of orthogonal symmetric higher bi-derivations on semiprime Г-ring is presented and studied and the relations of two symmetric higher bi-derivations on Г-ring are introduced.
Salih et al.
doaj   +1 more source