Let be a prime ring of characteristic different from 2, its right Martindale quotient ring and its extended centroid. Suppose that , are generalized skew derivations of with the same associated automorphism , and is a non-central polynomial over such that for all . Then there exists such that for all .
The purpose of this paper is to investigate identities satisfied by centralizers on prime and semiprime rings. We prove the following result: Let be a noncommutative prime ring of characteristic different from two and let and be left centralizers on . Suppose that is fulfilled for all . If
In this paper we investigate commutativity of ring with involution which admits a derivation satisfying certain algebraic identities on Jordan ideals of . Some related results for prime rings are also discussed. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.
We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which “controls” deformations of the structure bracket of the algebroid.
The goal of this paper is to provide some basic structure information on derivations in finite semirings.