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

Abstract

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

arXiv comment19 pages, Linear Algebra and its Applications 2017

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• $2$-Local derivations on von Neumann algebras
• 2-local derivations on semi-finite von Neumann algebras
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Cited by in corpus (2)

• Non-associative algebraic structures: classification and structure
• Local and $2$-local derivations of simple $n$-ary algebras