lie mappings on some matrix rings

We study lie derivations on trivial generalized matrix algebras (tg-algebras), i.e. block algebras of the form (n b a m) with mn = nm = 0, without assuming the existence of a unit. under natural hypotheses on the center and on faithfulness of the bimodules m; n, we show that every lie derivation can be decomposed into a sum of an associative derivation, a possible extremal lie part coming from the off-diagonal blocks, and a center-valued linear map annihilating all commutators. we state precise sufficient conditions for the absence of the extremal part and give illustrative examples.