Results 81 to 90 of about 1,309,327 (169)

Generalized Derivations in Semiprime Gamma Rings [PDF]

International Journal of Mathematics and Mathematical Sciences, 2012
LetMbe a 2-torsion-free semiprimeΓ-ring satisfying the conditionaαbβc=aβbαcfor alla,b,c∈M,  α,β∈Γ, and letD:M→Mbe an additive mapping such thatD(xαx)=D(x)αx+xαd(x)for allx∈M,  α∈Γand for some derivationdofM. We prove thatDis a generalized derivation.
Kalyan Kumar Dey, Akhil Chandra Paul, I. S. Rakhimov   +2 more
openaire   +3 more sources

Derivations on semiprime rings [PDF]

Bulletin of the Australian Mathematical Society, 1996
The main result: Let R be a 2-torson free semiprime ring and let D: R → R be a derivation. Suppose that [[D(x), x], x] = 0 holds for all x ∈ R. In this case [D(x), x] = 0 holds for all x ∈ R.
openaire   +1 more source

GENERALIZED JORDAN DERIVATIONS ON SEMIPRIME RINGS [PDF]

Journal of the Australian Mathematical Society, 2019
The purpose of this note is to prove the following. Suppose $\mathfrak{R}$ is a semiprime unity ring having an idempotent element $e$ ($e\neq 0,~e\neq 1$) which satisfies mild conditions. It is shown that every additive generalized Jordan derivation on $\mathfrak{R}$ is a generalized derivation.
Ferreira, Bruno L M, Guzzo Jr., Henrique, Ferreira, Ruth N.   +2 more
openaire   +2 more sources

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  

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

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

A Note on Power Values of Derivation in Prime and Semiprime Rings

Journal of Mathematical Extension, 2012
Let R be a ring with derivation d, such that (d(xy))n = (d(x))n (d(y))n for all x, y ∈ R and n > 1 a fixed integer. In this paper, we show that if R is prime, then d = 0 or R is commutative. If R is semiprime, then d maps R into its center. Moreover
Sh. Sahebi, V. Rahmani
doaj  

Soft ideals of soft ternary semigroups. [PDF]

Heliyon, 2021
Kar S, Dutta I.
europepmc   +1 more source

Fuzzy bipolar soft semiprime ideals in ordered semigroups. [PDF]

Heliyon, 2021
Aziz-Ul-Hakim, Khan H, Ahmad I, Khan A.
europepmc   +1 more source

The X-semiprimeness of rings

Journal of Algebra and Its Applications
For a nonempty subset [Formula: see text] of a ring [Formula: see text], the ring [Formula: see text] is called [Formula: see text]-semiprime if, given [Formula: see text], [Formula: see text] implies [Formula: see text]. This provides a proper class of semiprime rings. First, we clarify the relationship between idempotent semiprime and unit-semiprime
Grigore Călugăreanu, Tsiu-Kwen Lee, Jerzy Matczuk   +2 more
openaire   +2 more sources