Results 1 to 10 of about 104 (92)
On the primeness of near-rings [PDF]
Arab Journal of Mathematical Sciences, 2020 In this paper, we study the different kinds of the primeness on the class of near-rings and we give new characterizations for them. For that purpose, we introduce new concepts called set-divisors, ideal-divisors, etc.
Khalid H. Al-Shaalan
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ON COMMUTATIVITY OF PRIME NEAR RINGS [PDF]
Matrix Science Mathematic, 2021 In this paper, we prove commutativity of prime near rings by using the notion of β-derivations. Let M be a zero symmetric prime near ring. If there exist p ≥ 0, q ≥ 0 and a nonzero two sided β-derivation d on M, where β : M → M is a homomorphism, such ...
Abdul Rauf Khan +2 more
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Generalized Derivations on Prime Near Rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2013 Let N be a near ring. An additive mapping f:N→N is said to be a right generalized (resp., left generalized) derivation with associated derivation d on N if f(xy)=f(x)y+xd(y) (resp., f(xy)=d(x)y+xf(y)) for all x,y∈N.
Asma Ali, Howard E. Bell, Phool Miyan
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On Generalized Semiderivations of Prime Near Rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2015 Let N be a near ring. An additive mapping F:N→N is said to be a generalized semiderivation on N if there exists a semiderivation d:N→N associated with a function g:N→N such that F(xy)=F(x)y+g(x)d(y)=d(x)g(y)+xF(y) and F(g(x))=g(F(x)) for all x,y∈N.
Abdelkarim Boua +3 more
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On Prime Near-Rings with Generalized Derivation [PDF]
International Journal of Mathematics and Mathematical Sciences, 2008 Let N be a 3-prime 2-torsion-free zero-symmetric left near-ring with multiplicative center Z. We prove that if N admits a nonzero generalized derivation f such that f(N)⊆Z, then N is a commutative ring. We also discuss some related properties.
Howard E. Bell
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On prime and semiprime near-rings with derivations [PDF]
International Journal of Mathematics and Mathematical Sciences, 1997 Let N be a semiprime right near-ring, A a subset of N such that 0∈A and AN⫅A, and d a derivation of N The purpose of this paper is to prove that if d acts as a homomorphism on A or as an anti-homomorphism on A, then d(A)={0}.
Nurcan Argaç
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On Prime-Gamma-Near-Rings with Generalized Derivations [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 Let 𝑁 be a 2-torsion free prime Γ-near-ring with center 𝑍(𝑁). Let (𝑓,𝑑) and (𝑔,ℎ) be two generalized derivations on 𝑁. We prove the following results: (i) if 𝑓([𝑥,𝑦]𝛼)=0 or 𝑓([𝑥,𝑦]𝛼)=±[𝑥,𝑦]𝛼 or 𝑓2(𝑥)∈𝑍(𝑁) for all 𝑥,𝑦∈𝑁, 𝛼∈Γ, then 𝑁 is a commutative Γ ...
Kalyan Kumar Dey +2 more
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ON PRIME GAMMA-NEAR-RINGS WITH DERIVATIONS [PDF]
Communications of the Korean Mathematical Society, 2004 Summary: Conditions for a \(\Gamma\)-near-ring to be commutative are investigated.
Mustafa Uçkun, Young-Bae Jun
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ON SEMIDERIVATIONS IN 3-PRIME NEAR-RINGS
Communications of the Korean Mathematical Society, 2016 Abstract. In the present paper, we expand the domain of work on theconcept of semiderivations in 3-prime near-rings through the study ofstructure and commutativity of near-rings admitting semiderivations sat-isfying certain differential identities. Moreover, several examples havebeen provided at places which show that the assumptions in the hypothe-ses ...
Mohammad Ashraf, Boua Abdelkarim
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On derivations and commutativity in prime near-rings
Journal of Taibah University for Science, 2014 AbstractIn the present paper it is shown that zero symmetric prime right near-rings satisfying certain identities are commutative rings.
Boua Abdelkarim, Abderrahmane Raji
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