Results 1 to 10 of about 1,198,003 (194)

A Characterization of Semiprime Rings with Homoderivations

Journal of New Theory, 2023
This paper is focused on the commutativity of the laws of semiprime rings, which satisfy some algebraic identities involving homoderivations on ideals. It provides new and notable results that will interest researchers in this field, such as “R contains ...
Emine Koç Sögütcü
doaj   +5 more sources

A Note on Weakly Semiprime Ideals and Their Relationship to Prime Radical in Noncommutative Rings [PDF]

Journal of Mathematics
In this paper, we introduce the concept of weakly semiprime ideals and weakly n-systems in noncommutative rings. We establish the equivalence between an ideal P being a weakly semiprime ideal and R−P being a weakly n-system.
Alaa Abouhalaka
doaj   +3 more sources

On the Structure of Semiprime Rings [PDF]

Proceedings of the American Mathematical Society, 1973
The structure of prime rings has recently been studied by A. W. Goldie, R. E. Johnson, L. Lesieur and R. Croisot. In their main results some sort of finiteness assumption is invariably made. It is shown in this paper that certain semiprime rings are subdirect sums of full rings of linear transformations of a right vector space over a division ring.
Augusto H. Ortiz
openalex   +2 more sources

On Centrally Semiprime Rings and Centrally Semiprime [PDF]

Kirkuk Journal of Science, 2008
In this paper, two new algebraic structures are introduced which we call a centrally semiprime ring and a centrally semiprime right near-ring, and we look for those conditions which make centrally semiprime rings as commutative rings, so that several ...
Adil Kadir Jabbar, Abdulrahman Hamed Majeed   +1 more
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On the Multiplicative (Generalised) (α, α)−Derivations of Semiprime Rings

Journal of New Theory, 2022
The algebraic properties and identities of a semiprime ring are investigated with the help of the multiplicative (generalised)-(α, α)-reverse derivation on the non-empty ideal of the semiprime ring.
Neşet Aydın, Handan Karahan, Didem Yeşil   +2 more
doaj   +2 more sources

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 ...
R. E. Johnson, Lawrence S. Levy
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On Centrally Prime and Centrally Semiprime Rings [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics, 2008
In this paper, centrally prime and centrally semiprime rings are defined and the relations between these two rings and prime (resp. semiprime) rings are studied.Among the results of the paper some conditions are given under which prime (resp.
Adil Jabbar, Abdularahman Majeed
doaj   +2 more sources

A note on a pair of derivations of semiprime rings [PDF]

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   +2 more sources

On centralizers of semiprime rings [PDF]

Aequationes Mathematicae, 2003
The main result of this paper is the following. Let R be a 2-torsion free semiprime ring and let $ T : R \rightarrow R $ be an additive mapping such that $ 2T(xyx) = T(x)yx + xyT(x) $ holds for all $ x,y \in R $. Then T is a centralizer.
Joso Vukman, Irena Kosi-Ulbl
openalex   +3 more sources

Semiprime rings with generalized homoderivations

Boletim da Sociedade Paranaense de Matemática, 2022
This study develops some results involving generalized homoderivation in semiprime rings and investigates the commutativity of semiprime rings admitting generalized homoderivations of ring R satisfying certain identities and some related results have ...
Abdelkarim Boua, Emine Koç Sogutcu
doaj   +2 more sources