Results 21 to 30 of about 1,324,184 (168)

A note on derivations in semiprime rings [PDF]

International Journal of Mathematics and Mathematical Sciences, 2005
We prove in this note the following result. Let n>1 be an integer and let R be an n!-torsion-free semiprime ring with identity element. Suppose that there exists an additive mapping D:R→R such that D(xn)=∑j=1nxn−jD(x)xj−1 is fulfilled for all x∈R.
Joso Vukman, Irena Kosi-Ulbl
doaj   +3 more sources

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.
doaj   +2 more sources

S-Semiprime Submodules and S-Reduced Modules

Journal of Mathematics, 2020
This article introduces the concept of S-semiprime submodules which are a generalization of semiprime submodules and S-prime submodules. Let M be a nonzero unital R-module, where R is a commutative ring with a nonzero identity.
Ayten Pekin, Ünsal Tekir, Özge Kılıç   +2 more
doaj   +2 more sources

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
doaj   +2 more sources

D-Semiprime Rings

European Journal of Pure and Applied Mathematics
Let R be an associative and 2-torsion-free ring with an identity. in this work, we will generalize the results of differentially prime rings in [18] by applying the hypotheses in a differentially semiprime rings.
Maram Alosaimi, A. Alkhalaf, Rohaidah Masri, I. Taha   +3 more
semanticscholar   +2 more sources

Embeddings of semiprime rings into semisimple Artinian rings [PDF]

Journal of Algebra and its Applications, 2023
Goldie’s Theorem implies that a semiprime left Goldie ring is embeddable into a semisimple Artinian ring. On the other hand, there are domains that are not embeddable into division rings.
Volodymyr Bavula
semanticscholar   +1 more source

Source of semiprimeness of $\ast$-prime rings

Journal of Amasya University the Institute of Sciences and Technology
This study constructs a structure $S_{R}^{\ast}$ that had never been studied before and obtained new results by defining a subset $S_{R}^{\ast}$ of $R$ as$S_{R}^{\ast}=\left\{ \left.
Barış Albayrak, Didem Yeşil, Didem Karalarlıoğlu Camcı   +2 more
doaj   +4 more sources

Quasi-semiprime Modules

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
doaj   +1 more source

Generalized Munn rings

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
doaj   +1 more source

Minimal Prime and Semiprime Submodules

Babylonian Journal of Mathematics, 2023
Prime and semiprime submodules are important generalizations of prime and semiprime ideals to module theory over commutative rings. However, minimal or smallest prime/semiprime submodules have received comparatively less attention.
R. M. Al-Masroub, Mahmood S. Fiadh
semanticscholar   +1 more source