“…Motivated by the above results, in this section we explore the commutativity of a * -prime ring R in which the generalized derivation F satisfies similar identities on a * -Jordan ideal. We shall conclude this section with an application of our results which extend results of [8] and [9] to Jordan ideals with the additional assumption that the ring R be 2-torsion free.…”
“…Using similar arguments as used in the proof of Theorem 2.5, application of Theorem 3.1 yields the following result which extends ( [9], Theorem 3.7) and ( [8], Theorem 2.3) to Jordan ideals in the case of a 2-torsion free ring.…”
“…As an application of Theorem 2.4, the following theorem extends ( [9], Theorem 3.3) and ( [8], Theorem 2.1 ) to Jordan ideals. Moreover, if we set J = J × J, then J is a * ex -Jordan ideal of R and F [x, y] = [x, y] for all x, y ∈ J.…”
Section: Lemma ([3]mentioning
confidence: 91%
“…Reasoning as in the proof of Theorem 2.5, where F(x, y) = (F (x), −y), and using Theorem 2.6 we extend ( [9], Theorem 3.4) and ( [8], Theorem 2.2 ) to Jordan ideals as follows.…”
In this paper we investigate generalized derivations satisfying certain differential identities on Jordan ideals of rings with involution and discuss related results. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.
“…Motivated by the above results, in this section we explore the commutativity of a * -prime ring R in which the generalized derivation F satisfies similar identities on a * -Jordan ideal. We shall conclude this section with an application of our results which extend results of [8] and [9] to Jordan ideals with the additional assumption that the ring R be 2-torsion free.…”
“…Using similar arguments as used in the proof of Theorem 2.5, application of Theorem 3.1 yields the following result which extends ( [9], Theorem 3.7) and ( [8], Theorem 2.3) to Jordan ideals in the case of a 2-torsion free ring.…”
“…As an application of Theorem 2.4, the following theorem extends ( [9], Theorem 3.3) and ( [8], Theorem 2.1 ) to Jordan ideals. Moreover, if we set J = J × J, then J is a * ex -Jordan ideal of R and F [x, y] = [x, y] for all x, y ∈ J.…”
Section: Lemma ([3]mentioning
confidence: 91%
“…Reasoning as in the proof of Theorem 2.5, where F(x, y) = (F (x), −y), and using Theorem 2.6 we extend ( [9], Theorem 3.4) and ( [8], Theorem 2.2 ) to Jordan ideals as follows.…”
In this paper we investigate generalized derivations satisfying certain differential identities on Jordan ideals of rings with involution and discuss related results. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.
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.
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