Two-Local derivations on associative and Jordan matrix rings over commutative rings

摘要

In the present paper we prove that every 2-local inner derivation on thematrix ring over a commutative ring is an inner derivation and every derivationon an associative ring has an extension to a derivation on the matrix ring overthis associative ring. We also develop a Jordan analog of the above method andprove that every 2-local inner derivation on the Jordan matrix ring over acommutative ring is a derivation.