2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW-algebras

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The paper is devoted to 2-local derivations on matrix algebras over unital semi-prime Banach algebras. For a unital semi-prime Banach algebra A with the inner derivation property we prove that any 2-local derivation on the algebra M₂ₙ(A), n≥ 2, is a derivation. We apply this result to AW-algebras and show that any 2-local derivation on an arbitrary AW-algebra is a derivation.