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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.
The purpose of this paper is to prove the following result: Let be a -torsion free semiprime ring and let be an additive mapping, such that holds for all . In this case is left and right centralizer.
Let be a prime ring of characteristic different from , the Utumi quotient ring of , the extended centroid of , a non-central Lie ideal of , a non-zero generalized derivation of . Suppose that for all , then one of the following holds: (1) there exists such that for all ; (2) satisfies the standard identity and there exist and such that for all . We also extend the result to the one-sided case. Finally, as an application we obtain some range inclusion results of...
Let be a prime ring of characteristic different from 2 and 3, its right Martindale quotient ring, its extended centroid, a non-central Lie ideal of and a fixed positive integer. Let be an automorphism of the ring . An additive map is called an -derivation (or a skew derivation) on if for all . An additive mapping is called a generalized -derivation (or a generalized skew derivation) on if there exists a skew derivation on such that for all . We prove that, if ...
We show that there exist zero-symmetric simple nearrings with identity, which are not equiprime, solving a longstanding open problem.
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