A result concerning additive mappings in semiprime rings

Year, pages: 2015, 1271 - 1276

In this paper we prove the following result. Let $R$ be a $2$-torsion free semiprime ring and let $f:R\rightarrow R$ be an additive mapping satisfying the relation $f(x)x²+x²f(x)=0$ for all $x\in R$. In this case $f=0$. Any semisimple Banach algebra (for example, $C^*$ algebra) is semiprime. Therefore this algebraic result might be of some interest from functional analysis point of view.

Fošner, M. 2015. A result concerning additive mappings in semiprime rings. In Mathematica Slovaca, vol. 65, no.6, pp. 1271-1276. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0088

Fošner, M. (2015). A result concerning additive mappings in semiprime rings. Mathematica Slovaca, 65(6), 1271-1276. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0088