On a certain functional identity involving inverses

ABSTRACT

Let R be a simple artinian ring with characteristic different from 2 and 3. The purpose of this paper is to describe additive maps f,g satisfying the identity $f\left(x\right)x^{-1}+xg\left(x^{-1}\right)=0$ for every invertible x∈R.

KEYWORDS:

• Division ring
• functional identity

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16R60

Acknowledgements

The author would like to thank Dr. Mikhail A. Chebotar for his guidance and assistance. The author would also like to thank the referee for his/her useful suggestions.