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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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Homoderivations and semigroup ideals in 3-prime near-rings

2021
Summary: This paper studies homoderivations satisfying certain conditions on semigroup ideals of near-rings. In addition, we include some examples of the necessity of the hypotheses used in our results.
Mouhssine, Samir, Boua, Abdelkarim
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On generalized semiderivations in 3-prime near-rings

Asian-European Journal of Mathematics, 2016
There is a large body of evidence showing that the existence of a suitably-constrained derivation on a 3-prime near-ring forces the near-ring to be a commutative ring. The purpose of this paper is to study generalized semiderivations which satisfy certain identities on 3-prime near-ring and generalize some results due to [H. E. Bell and G.
Boua, A., Oukhtite, L., Raji, A.
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On multiplicative generalized derivations in 3-prime near-rings

AIP Conference Proceedings, 2018
In the present paper, we prove that 3–prime near-ring N is commutative ring, if any one of the following conditions are satisfied: (i) f (N) ⊆ Z, (ii) f ([x, y]) = 0, (iii) f ([x, y]) = ±τ ([x, y]), (iv) f ([x, y]) = ±τ(xoy), (v) f ([x, y]) = τ ([d(x), y]), for all x, y ∈ N, where f is a nonzero left multiplicative generalized (σ, τ)-derivation of N ...
Bedir, Zeliha, Golbas, Oznur
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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.
openaire   +1 more source

Results on 3-prime near-rings with generalized derivations

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohammad Ashraf, Mohammad Aslam Siddeeque   +1 more
openaire   +2 more sources

Left generalized homoderivations in 3-prime near-rings

Journal of Discrete Mathematical Sciences and Cryptography
In this paper, the structure of 3-prime near-rings with left generalized homoderivation satisfying certain conditions on a semigroup ideal will be investigated. After that, we’ll provide examples to explain why the hypotheses used in the various results are necessary.
Samir Mouhssine, Abdelkarim Boua
openaire   +1 more source