Identities related to generalized derivation on ideal in prime rings

Abstract

Let R be a prime ring with center Z (R), I a non-zero ideal of R and α : R → R any mapping on R. Suppose that G and F are two generalized derivations associated with derivations g and d respectively on R.

A study of derivable mappings of semiprime rings

“…Pre-multiply ( 17) by z and subtract it from (18) in order to find Similarly, with some necessary variations we can prove the same conclusions for G(uv…”

“…Thus, it would be a fact of interest to prove the results of generalized derivations for multiplicative (generalized)-derivations. Recently, a number of results involving multiplicative (generalized)derivations has been obtain (see [10,14,15,18] and references therein). Tiwari et.…”

“…al. [18] studied the following identities involving generalized derivations on some appropriate subsets of prime rings:…”

Remarks on Derivable Maps of Semi-prime Rings

“…Thus, it would be a fact of interest to prove the results of generalized derivation for multiplicative (generalized)derivations. In this direction many results has been obtained during last five years (see [6,[12][13][14]). Recently, Tiwari et al [12] studied the following identities involving generalized derivations on some appropriate subsets of prime rings:…”

Generalized derivations on Lie ideals in prime rings

“…Let R be a prime ring, I an ideal of R, α a map on R, and G, F be two generalized derivations on R. Tiwari et al [15], studied the commutativity of such a ring if anyone of the following is central:…”