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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...
Let be a semiprime ring with unity and , be automorphisms of . In this paper it is shown that if satisfies
for all and some fixed integer , then is an (, )-derivation. Moreover, this result makes it possible to prove that if admits an additive mappings satisfying the relations
for all and some fixed integer , then and are (, )derivations under some torsion restriction. Finally, we apply these purely ring theoretic results to semi-simple Banach algebras.
We investigate 2-local Jordan automorphisms on operator algebras. In particular, we show that every 2-local Jordan automorphism of the algebra of all n× n real or complex matrices is either an automorphism or an anti-automorphism. The same is true for 2-local Jordan automorphisms of any subalgebra of ℬ which contains the ideal of all compact operators on X, where X is a real or complex separable Banach spaces and ℬ is the algebra of all bounded linear operators on X.
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