  The paper is devoted to 2-local derivations on matrix algebras over
commutative regular algebras. We give necessary and sufficient conditions on a
commutative regular algebra to admit 2-local derivations which are not
derivations. We prove that every 2-local derivation on a matrix algebra over a
commutative regular algebra is a derivation. We apply these results to 2-local
derivations on algebras of measurable and locally measurable operators
affiliated with type I von Neumann algebras.
