Derivations and 2-local derivations on matrix algebras over commutative algebras
نویسندگان
چکیده
We characterize derivations and 2-local derivations from Mn(A) into Mn(M), n ≥ 2, where A is a unital algebra over C and M is a unital A-bimodule. We show that every derivation D : Mn(A) → Mn(M), n ≥ 2, is the sum of an inner derivation and a derivation induced by a derivation from A to M. We say that A commutes with M if am = ma for every a ∈ A and m ∈ M. If A commutes with M we prove that every inner 2-local derivation D : Mn(A) → Mn(M), n ≥ 2, is an inner derivation. In addition, if A is commutative and commutes with M, then every 2-local derivation D : Mn(A) → Mn(M), n ≥ 2, is a derivation.
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