Additivity of Jordan (Triple) Derivations on Rings

Abstract

Abstract. Let δ be a mapping from ring R into itself satisfyingUnder some conditions on R, we show that δ is additive.

Jordan Higher Derivable Mappings on Rings

“…Motivated by the above result due to Lu [2], in the year 2011, Jing and Lu [3] characterized Jordan derivable maps to a larger class of rings and proved the following theorem.…”

“…Theorem 1 (see [3,Theorem 1.2]). Let be a ring containing a nontrivial idempotent and satisfying the following conditions for , , ∈ {1, 2}.…”

On Jordan Triple Higher Derivable Mappings on Rings

“…One of the result in this direction is given by Jing and Lu [11] in the year 2011. They characterized Jordan triple derivable maps to a larger class of rings and proved the following theorem: …”

“…We refer the readers to some recent papers [5,[11][12][13][14][15] where further references can be found. The aim of this paper is to initiate the study of Jordan triple higher derivable maps on certain classes of rings and provide a sufficient condition on a ring R under which a Jordan triple higher derivable map becomes a higher derivation.…”

“…Applying Lemma 1.6 of [11] and the well-known result that every Jordan triple higher derivation on a prime ring of characteristic different from two is a higher derivation (see [6]), we find the following: We shall conclude by giving an application of Theorem 2.1 in operator algebras. Since every standard operator algebra is prime, we can easily have: …”