Multiplicative Jordan n-higher derivations on alternative rings containing idempotents

Abstract

Suppose [Formula: see text] is an alternative ring containing a non-trivial idempotent and [Formula: see text] be a mapping from [Formula: see text] into itself. In this paper, we study the Jordan n-higher derivations on alternative rings and prove that under some mild conditions every multiplicative Jordan n-higher derivations on [Formula: see text] is additive. It is to be noted that the similarity to the notions is only in its written form, but not in its theoretical structures, because the Pierce decomposition used in the results for alternative rings is the generalization of the Pierce decomposition for associative rings.