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

##
*Mohammad
Ashraf, Asma Ali and Shakir
Ali*

**Address.**

Department of Mathematics,
Aligarh Muslim University, Aligarh 202002, India

**E-mail. ** mashraf80@hotmail.com

**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.

**AMSclassification. **16W25, 16Y30.

**Keywords. **prime near-ring, derivation, $\sigma$-derivation,
$(\sigma, \tau)$-derivation, $(\sigma, \tau)$-commuting derivation.