Geodesic
$(\sigma,\tau)$-derivations on prime near rings
Archivum mathematicum, Tome 40 (2004) no. 3, pp. 281-286 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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There is an increasing body of evidence that prime near-rings with derivations have ring like behavior, indeed, there are several results (see for example [1], [2], [3], [4], [5] and [8]) asserting that the existence of a suitably-constrained derivation on a prime near-ring forces the near-ring to be a ring. It is our purpose to explore further this ring like behaviour. In this paper we generalize some of the results due to Bell and Mason [4] on near-rings admitting a special type of derivation namely $(\sigma ,\tau )$- derivation where $\sigma ,\tau $ are automorphisms of the near-ring. Finally, it is shown that under appropriate additional hypothesis a near-ring must be a commutative ring.
There is an increasing body of evidence that prime near-rings with derivations have ring like behavior, indeed, there are several results (see for example [1], [2], [3], [4], [5] and [8]) asserting that the existence of a suitably-constrained derivation on a prime near-ring forces the near-ring to be a ring. It is our purpose to explore further this ring like behaviour. In this paper we generalize some of the results due to Bell and Mason [4] on near-rings admitting a special type of derivation namely $(\sigma ,\tau )$- derivation where $\sigma ,\tau $ are automorphisms of the near-ring. Finally, it is shown that under appropriate additional hypothesis a near-ring must be a commutative ring.
Classification : 16U70, 16W25, 16Y30
Keywords: prime near-ring; derivation; $\sigma $-derivation; $(\sigma, \tau )$-derivation; $(\sigma, \tau )$-commuting derivation 
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     author = {Ashraf, Mohammad and Ali, Asma and Ali, Shakir},
     title = {$(\sigma,\tau)$-derivations on prime near rings},
     journal = {Archivum mathematicum},
     pages = {281--286},
     year = {2004},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2004_40_3_a7/}
}
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Ashraf, Mohammad; Ali, Asma; Ali, Shakir. $(\sigma,\tau)$-derivations on prime near rings. Archivum mathematicum, Tome 40 (2004) no. 3, pp. 281-286. http://geodesic.mathdoc.fr/item/ARM_2004_40_3_a7/

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