2-Local derivations on matrix rings over associative rings

arXiv1303.6033MaRDI QIDQ6240607

Farhodjon Arzikulov, Sh. Ayupov

Publication date: 25 March 2013

Abstract: In the present paper it is proved that every inner 2-local derivation on the matrix ring $M_n(Re)$ of $nimesn$ matrices over a commutative associative ring $Re$ is an inner derivation. Also, it is proved that, every derivation on an associative ring $Re$ has an extension to a derivation on the matrix ring $M_n(Re)$ of $nimesn$ matrices over $Re$.

Mathematics Subject Classification ID

Commutators, derivations, elementary operators, etc. (47B47) Derivations, actions of Lie algebras (16W25) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57)

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