Some Results On Lie Ideal Of Prime Rings

As a new and important branch of ring theory, generalized polynomial identities(GPIs) play a key role in the development of modern mathematics. Since Posner's well-known paper appeared in 1957, the research of derivation, generalized derivation, symmetric biderivation, and etc, in prime rings has become an important field in the theory of ring. Especially over the last twenty years, a lot of work has been done in the research of derivation, generalized derivation acting on various subset of prime ring and the prime ring with involution, and also a lot of crucial results have been achieved. In this paper,we will main discuss the problem about derivation, generalized derivation which acted on Lie ideal of prime ring. To be more precise, we consider a prime ring R with characteristic different from two and extend some results concerning derivations, generalized derivations and symmetric biderivations of prime rings in either an ideal of R or the whole ring R to a square closed Lie ideal U of R.