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The $X$-semiprimeness of Rings [PDF]
arXivFor a nonempty subset $X$ of a ring $R$, the ring $R$ is called $X$-semiprime if, given $a\in R$, $aXa=0$ implies $a=0$. This provides a proper class of semiprime rings. First, we clarify the relationship between idempotent semiprime and unit-semiprime rings.
Grigore Călugăreanu +2 more
arxiv +3 more sources
Commutativity with Derivations of Semiprime Rings
Discussiones Mathematicae - General Algebra and Applications, 2020 Let R be a 2-torsion free semiprime ring with the centre Z(R), U be a non-zero ideal and d: R → R be a derivation mapping.
Atteya Mehsin Jabel
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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
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DERIVATIONS OF PRIME AND SEMIPRIME RINGS [PDF]
Journal of the Korean Mathematical Society, 2009 Let R be a prime ring, I a nonzero ideal of R, d a derivation of R and n a fixed positive integer. (i) If (d(x)y+xd(y)+d(y)x+yd(x)) n = xy + yx for all x,y 2 I, then R is commutative. (ii) If charR 6 2 and (d(x)y + xd(y) + d(y)x + yd(x)) n i (xy + yx) is central for all x,y 2 I, then R is commutative.
Nurcan Argaç, Hülya İnceboz
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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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Centralizing -Homoderivations of Semiprime Rings
Journal of mathematics, 2022 We introduce the notion of n -homoderivation on a ring ℜ and show that a ...
M. T. El-Sayiad, A. Ageeb, A. Ghareeb
semanticscholar +1 more source
Semiprimeness of semigroup algebras [PDF]
Open Mathematics, 2021 AbstractAbundant semigroups originate from p.p. rings and are generalizations of regular semigroups. The main aim of this paper is to study the primeness and the primitivity of abundant semigroup algebras. We introduce and studyD∗{{\mathcal{D}}}^{\ast }-graphs and Fountain matrices of a semigroup.
Junying Guo, Xiaojiang Guo
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Centrally Extended -Homoderivations on Prime and Semiprime Rings
Journal of mathematics, 2022 We present a new type of mappings called centrally extended α -homoderivations of a ring ℜ
Mahmoud M. El-Soufi, A. Ghareeb
semanticscholar +1 more source
Exploring Hybrid H-bi-Ideals in Hemirings: Characterizations and Applications in Decision Making
Mathematics, 2023 The concept of the hybrid structure, as an extension of both soft sets and fuzzy sets, has gained significant attention in various mathematical and decision-making domains.
Asmat Hadi +5 more
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