# $(\sigma ,\tau )$-derivations on prime near rings

Mohammad Ashraf; Asma Ali; Shakir Ali

Archivum Mathematicum (2004)

- Volume: 040, Issue: 3, page 281-286
- ISSN: 0044-8753

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topAshraf, Mohammad, Ali, Asma, and Ali, Shakir. "$(\sigma ,\tau )$-derivations on prime near rings." Archivum Mathematicum 040.3 (2004): 281-286. <http://eudml.org/doc/249295>.

@article{Ashraf2004,

abstract = {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.},

author = {Ashraf, Mohammad, Ali, Asma, Ali, Shakir},

journal = {Archivum Mathematicum},

keywords = {prime near-ring; derivation; $\sigma $-derivation; $(\sigma , \tau )$-derivation; $(\sigma , \tau )$-commuting derivation; prime near-rings; commuting derivations; commutativity theorems},

language = {eng},

number = {3},

pages = {281-286},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {$(\sigma ,\tau )$-derivations on prime near rings},

url = {http://eudml.org/doc/249295},

volume = {040},

year = {2004},

}

TY - JOUR

AU - Ashraf, Mohammad

AU - Ali, Asma

AU - Ali, Shakir

TI - $(\sigma ,\tau )$-derivations on prime near rings

JO - Archivum Mathematicum

PY - 2004

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 040

IS - 3

SP - 281

EP - 286

AB - 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.

LA - eng

KW - prime near-ring; derivation; $\sigma $-derivation; $(\sigma , \tau )$-derivation; $(\sigma , \tau )$-commuting derivation; prime near-rings; commuting derivations; commutativity theorems

UR - http://eudml.org/doc/249295

ER -

## References

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- Kamal Ahmad A. M., $\sigma $- derivations on prime near-rings, Tamkang J. Math. 32 2 (2001), 89–93. MR1826415
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- Posner E. C., Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100. (1957) MR0095863
- Wang X. K., Derivations in prime near-rings, Proc. Amer. Math. Soc. 121 (1994), 361–366. (1994) Zbl0811.16040MR1181177

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