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A Note on Weakly Semiprime Ideals and Their Relationship to Prime Radical in Noncommutative Rings
Journal of MathematicsIn 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
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On Semiprime Goldie Modules [PDF]
Communications in Algebra, 2016 For an $R$-module $M$, projective in $\sigma[M]$ and satisfying ascending chain condition (ACC) on left annihilators, we introduce the concept of Goldie module. We also use the concept of semiprime module defined by Raggi et. al. in \cite{S} to give necessary and sufficient conditions for an $R$-module $M$, to be a semiprime Goldie module. This theorem
Jaime Castro Pérez +3 more
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Semiprime Novikov algebras [PDF]
International Journal of Algebra and Computation, 2022 We study prime and semiprime Novikov algebras. We prove that prime nonassociative Novikov algebra has zero nucleus and center. It is well known that an ideal of an alternative semiprime algebra is semiprime algebra. We proved this statement for Novikov algebras. It implies that a Baer radical exists in a class of Novikov algebras.
A. Panasenko
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On -Quasi-Semiprime Submodules [PDF]
The Eurasia Proceedings of Science Technology Engineering and Mathematics, 2023 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.
AL-ZOUBİ, Khaldoun, ALGHUEIRI, Shatha
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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 +1 more
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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
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The wreath product of semiprime skew braces is semiprime [PDF]
Communications in Algebra, 2020 In this note, we show that the wreath product of two semiprime skew braces is also a semiprime skew brace.
Patrick I. Kinnear
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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
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Graded semiprime multiplication modules
Boletim da Sociedade Paranaense de Matemática, 2020 Let $M$ be a $G$-graded $R$-module. In this article, we introduce the concept of graded semiprime multiplication modules. A graded $R$-module $M$ is said to be graded semiprime multiplication if $M$ has no graded semiprime $R$-submodules or for every ...
Rashid Abu-Dawwas
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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
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