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Original scientific paper

https://doi.org/10.3336/gm.53.1.06

A result in the spirit of Herstein theorem

Maja Fošner ; Faculty of logistics, University of Maribor, Mariborska cesta 7, 3000 Celje, Slovenia
Benjamin Marcen ; Faculty of logistics, University of Maribor, Mariborska cesta 7, 3000 Celje, Slovenia
Joso Vukman ; Institute of mathematics, physics and mechanics, Jadranska 19, 1000 Ljubljana, Slovenia


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Abstract

A classical result of Herstein asserts that any Jordan derivation on a prime ring of characteristic different from two is a derivation. It is our aim in this paper to prove the following result, which is in the spirit of Herstein's theorem. Let n3 be some fixed integer, let R be a prime ring with char(R)>4n8 and let D:R → R be an additive mapping satisfying either the relation D(xn)=D(xn1)x+xn1D(x) or the relation D(xn)=D(x)xn1+xD(xn1) for all xR. In both cases D is a derivation.

Keywords

Prime ring; semiprime ring; derivation; Jordan derivation; functional identity

Hrčak ID:

201813

URI

https://hrcak.srce.hr/201813

Publication date:

20.6.2018.

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