On Derivations in Near-Rings

Bell, Howard E.; Mason, Gordon

doi:10.1016/s0304-0208(08)72283-7

Cited by 121 publications

(84 citation statements)

References 3 publications

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“…As for terminologies concerning near-rings used here without special mention, we refer to G. Pilz [10]. Derivations and bi-derivations in rings and near-rings have been studied by many mathematicians in several ways [1,2,3,4,5,6,7,8,11,12,15,16]. Furthermore, M. Uçkun and M.A.Öztürk [14] investigated symmetric bi-Γ-derivations and commutativity in Γ-near-rings.…”

Section: A Non-empty Set R With Two Binary Operations + (Addition) Anmentioning

confidence: 99%

On Symmetric Generalized 3-Derivations and Commutativity in Prime Near-Rings

Park¹,

Jung²

2009

Honam Mathematical Journal

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Section: A Non-empty Set R With Two Binary Operations + (Addition) Anmentioning

confidence: 99%

On Symmetric Generalized 3-Derivations and Commutativity in Prime Near-Rings

Park¹,

Jung²

2009

Honam Mathematical Journal

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“…The purpose of this paper is to study derivations on TV. We show two main results: ( 1 ) Let N be 2-torsion-free, and let Dx and Di be derivations on TV suchthat D\D2 is also a derivation. Then either D\ or Di is zero if and only if [Dx(x), D2(y)] = 0 for all x, y 6 TV.…”

Section: Derivations In Prime Near-rings Xue-kuan Wang (Communicated mentioning

confidence: 99%

Derivations in Prime Near-Rings

Wang

1994

Proceedings of the American Mathematical Society

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Abstract. Let N be a prime near-ring with center Z . The purpose of this paper is to study derivations on TV. We show two main results: ( 1 ) Let N be 2-torsion-free, and let Dx and Di be derivations on TV suchthat D\D2 is also a derivation. Then either D\ or Di is zero if and only if [Dx(x), D2(y)] = 0 for all x, y 6 TV. (2) Let n be an integer > 1 , TV be n!-torsion-free, and D a derivation with D"(N) = {0} . Then D(Z) = {0} .

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“…There are many authors who studied derivations in various algebraic structures, such as rings, lattices, BCI-algebra and subtraction algebras, etc [11][12][13][14][15]. In [16], we introduced the notion of derivation for a quantale, and we discussed some related properties.…”

Section: Introductionmentioning

confidence: 99%

On derivations of quantales

Xiao

Liu

2016

Open Mathematics

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A quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It's well known that quantic nucleus and quantic conucleus play important roles in a quantale. In this paper, the relationships between derivation and quantic nucleus (conucleus) are studied via introducing the concept of pre-derivation.

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On Derivations in Near-Rings

Cited by 121 publications

References 3 publications

On Symmetric Generalized 3-Derivations and Commutativity in Prime Near-Rings

On Symmetric Generalized 3-Derivations and Commutativity in Prime Near-Rings

Derivations in Prime Near-Rings

On derivations of quantales

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