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arXiv · 2108.03993

2-Local and local derivations on Jordan matrix rings over commutative involutive rings

Sh. A. Ayupov·F. N. Arzikulov·N. M. Umrzaqov·O. O. Nuriddinov
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Abstract

In the present paper we prove that every 2-local inner derivation on the Jordan ring of self-adjoint matrices over a commutative involutive ring is a derivation. We also apply our technique to various Jordan algebras of infinite dimensional self-adjoint matrix-valued maps on a set and prove that every 2-local spatial derivation on such algebras is a spatial derivation. It is also proved that every local spatial derivation on the same Jordan algebras is a derivation.

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Sh. A. Ayupov, F. N. Arzikulov, N. M. Umrzaqov, O. O. Nuriddinov. 2021-07-25. 2-Local and local derivations on Jordan matrix rings over commutative involutive rings. https://arxiv.org/abs/2108.03993

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