Identities with inverses on matrix rings
Makaleler > Tam Makale · 2019
Yazarlar: N. Argaç, M. P. Eroǧlu, T.-K. Lee, J.-H. Lin
Linear and Multilinear Algebra, Uluslararası, Wos, 2019, cilt 68, ss 635-651
DOI: 10.1080/03081087.2019.1575331
Özet
Motivated by [1, 2], the goal of the paper is to study certain identities with inverses on matrix rings. Given D a division ring, we characterize additive maps f,g:D→D satisfying the identity f(x)x−1+xg(x−1)=0 for all invertible x∈D. Let R be a matrix ring over a division ring of characteristic not 2. We also characterize additive maps f,g:R→R satisfying the identity f(x)x−1+xg(x−1)=0 for all invertible x∈R. Precisely, there exist an element q∈R and a derivation d of R such that f(x)=xq+d(x) and g(x)=−qx+d(x) for all x∈R. This affirmatively answers the question below Theorem 4 in [1] due to L. Catalano.