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Functional equations related to higher derivations in semiprime rings
Open Mathematics, 2021 We investigate the additivity and multiplicativity of centrally extended higher derivations and show that every centrally extended higher derivation of a semiprime ring with no nonzero central ideals is a higher derivation.
Ezzat O. H.
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Semiprime rings with nilpotent Lie ring of inner derivations
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2014 We give an elementary and self-contained proof of the theorem which says that for a semiprime ring commutativity, Lie-nilpotency, and nilpotency of the Lie ring of inner derivations are equivalent conditions.
Kamil Kular
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Semiprime rings with Krull dimension are Goldie
Journal of Algebra, 1973 Robert Gordon, J. C. Robson
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Ibn Al-Haitham Journal for Pure and Applied Sciences, 2023 Suppose that A be an abelain ring with identity, B be a unitary (left) A-module, in this paper ,we introduce a type of modules ,namely Quasi-semiprime A-module, whenever is a Prime Ideal For proper submodule N of B,then B is called Quasi ...
Muntaha Abdul- Razaq Hasan
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Open Mathematics, 2022 Generalized Munn rings exist extensively in the theory of rings. The aim of this note is to answer when a generalized Munn ring is primitive (semiprimitive, semiprime and prime, respectively).
Guo Junying, Guo Xiaojiang
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Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1991 AbstractSome properties of v-semiprime (v = 0, 1, 2) near-rings are pointed out. In particular v semiprime near-rings which contain nil non-nilpotent ideals are studied.
S. De Stefano, S. Di Sieno
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On -Quasi-Semiprime Submodules [PDF]
The eurasia proceedings of science, technology, engineering & mathematics, 2021 Let G be a group. A ring R is called a graded ring (or G-graded ring) if there exist additive subgroups Rα of R indexed by the elements α∈G such that R=⊕α∈GRαand RαRβ⊆Rαβ for all α, β∈G.
K. Al-Zoubi, Shatha Alghueiri
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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
Günter Törner, R. Mazurek
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Multiplicative (Generalized) Reverse Derivations on Semiprime Ring
European Journal of Pure and Applied Mathematics, 2018 Let R be a semiprime ring. A mapping F : R → R (not necessarily additive) is called a multiplicative (generalized) reverse derivation if there exists a map  d : R → R (not necessarily a derivation nor an additive map) such that F(xy) = F(y)x +
Asma Ali, Ambreen Bano
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