Results 81 to 90 of about 2,863 (195)
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 +2 more
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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
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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.
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Karpatsʹkì Matematičnì Publìkacìï, 2014 We prove that in a ring $R$ with an identity there exists an element $a\in R$ and a nonzero derivation $d\in Der R$ such that $ad(a)\neq 0$. A ring $R$ is said to be a $d$-rigid ring for some derivation $d \in Der R$ if $d(a)=0$ or $ad(a)\neq 0$ for all
O.D. Artemovych, M.P. Lukashenko
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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 +2 more
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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
Prime Structures in a Morita Context
, 2018 In this paper, we study on the primeness and semiprimeness of a Morita context related to the rings and modules. Necessary and sufficient conditions are investigated for an ideal of a Morita context to be a prime ideal and a semiprime ideal.
Calci, Mete Burak +3 more
core
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.
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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
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