科研之友
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摘要
Let R be a commutative ring with identity and A be a unital algebra with nontrivial idempotent e over R. Motivated by Benkovi. c's systematic and powerful work [2, 3, 4, 5, 6, 7, 8], we will study multiplicative Lie higher derivations (i.e. those Lie higher derivations without additivity assumption) on A in this article. Let D = {L-k}(k is an element of N) be a multiplicative Lie higher derivation on A. It is shown that under suitable assumptions, D = {L-k}(k is an element of N) is of standard form; i. e. each component L-k (k >= 1) can be expressed through an additive higher derivation and a central mapping vanishing on all commutators of A.
