# 2-Local derivations on matrix algebras over commutative regular algebras

Source: [2-Local derivations on matrix algebras over commutative regular algebras](<https://www.sota2.com/research/paper/68fa50361e209131ce9699c4>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:55:28.925Z

Authors: Sh. A. Ayupov, K. K. Kudaybergenov, A. K. Alauadinov

Published: 2012-10-06T01:07:27.000Z

## Abstract

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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1210.1900>)

[PDF](<https://arxiv.org/pdf/1210.1900.pdf>)