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Focused Ultrasound Ablation for Neurological Disorders. [PDF]

Biol Psychiatry
Berton HS, Ray HD, Silva N, Boerwinkle VL, Dayton P, Roque D, Krishna V.   +6 more
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Altering the Fluorination Anodization Pathway of Silicon Near an Electrolyte Freezing Point Promotes the Formation of Blue-Photoluminescent Microstructures. [PDF]

ACS Appl Mater Interfaces
Chiou YS, Cheng CC, Li RW, Lee BT.
europepmc   +1 more source

Generalized multiplicative derivations in 3-prime near rings [PDF]

Mathematica Slovaca, 2018
Abstract In the present paper, we introduce the notion of generalized multiplicative derivation in a near-ring N and investigate commutativity of 3-prime near-rings, showing that certain conditions involving generalized multiplicative derivations force N to be a commutative ring.
Mohammad Ashraf, Abdelkarim Boua, Mohammad Aslam Siddeeque   +2 more
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On multiplicative derivations in 3-prime near-rings

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2023
A nearring \(N\) is called 3-prime if \(xNy=0\) implies \(x=0\) or \(y=0\). A multiplicative derivation is a map \(d:N\to N\) with \(d(xy)=xd(y)+ d(x)y\). Note that additivity is not required. Let \(N\) be a 3-prime nearring. The author shows that under various conditions, the existence of non-zero multiplicative derivations enforce \(N\) to be a ...
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SEVERAL ALGEBRAIC INEQUALITIES ON A 3-PRIME NEAR-RING

JP Journal of Algebra, Number Theory and Applications, 2017
Summary: The purpose of this paper is to study a bi-two sided a-derivation satisfying certain identities on a 3-prime near-ring.
Boua, A., Raji, A.
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Semigroup Ideals and Commutativity in 3-prime Near Rings

Communications in Algebra, 2015
The purpose of this paper is to study derivations and generalized derivations satisfying certain identities on semigroup ideals of near-rings. Some well-known results characterizing commutativity of 3-prime near-rings by derivations have been generalized by using semigroup ideals.
H. E. Bell, A. Boua, L. Oukhtite
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Generalized (α, β)-derivations in 3-prime near-rings

Journal of Discrete Mathematical Sciences & Cryptography, 2023
Let  be a 3-prime near-ring and  are endomorphisms. In this paper, we generalize a few results concerning generalized derivations and two sided α -generalized derivations of 3-prime near rings to generalized (α, β) -derivations. Cases demonstrating the need of the 3-primeness speculation is given. When  (resp.
Abdelkarim Boua, Ahmed Y. Abdelwanis
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LIE IDEALS AND JORDAN IDEALS IN 3-PRIME NEAR-RINGS WITH DERIVATIONS

JP Journal of Algebra, Number Theory and Applications, 2015
Let \(N\) be a zero-symmetric near-ring with multiplicative center \(Z(N)\). Define a Jordan (resp. Lie) ideal of \(N\) to be an additive subgroup \(J\) (resp. \(U\)) such that \(jx+xj\) and \(xj+jx\) are in \(J\) for all \(j\in J\) and \(x\in N\) (resp. \(ux-xu\in U\) for all \(u\in U\) and \(x\in N\)).
Boua, Abdelkarim, Kamal, Ahmed A. M.
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ON P-3-PRIME AND P-c-PRIME IDEALS IN NEAR-RINGS

JP Journal of Algebra, Number Theory and Applications, 2019
Summary: In this study, we introduce the concept of \(P\)-3-prime ideal for an ideal \(P\) of a near-ring. Then, the relations between \(P\)-3-prime ideal and \(P\)-\(c\)-prime ideal are obtained. It is proved that a \(P\)-\(c\)-prime ideal is a \(P\)-3-prime ideal. But, in general, the converse relation does not hold.
Taşdemir, Funda, Taştekin, İsmail
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Generalized multiplicative derivations and commutativity of 3-prime near-rings

Afrika Matematika, 2019
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Mohammad Ashraf, Mohammad Aslam Siddeeque   +1 more
openaire   +2 more sources