Identities with inverses on matrix rings

Argac N., Eroglu M. P., Lee T. -., Lin J. -.

LINEAR & MULTILINEAR ALGEBRA, cilt.68, sa.3, ss.635-651, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 68 Sayı: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1080/03081087.2019.1575331
  • Dergi Adı: LINEAR & MULTILINEAR ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.635-651
  • Anahtar Kelimeler: Division ring, derivation, inverse, matrix ring, functional identity
  • Dokuz Eylül Üniversitesi Adresli: Evet

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 is an element of 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 is an element of R. Precisely, there exist an element q is an element of R and a derivation d of R such that f(x)=xq+d(x) and g(x)=-qx+d(x) for all x is an element of R. This affirmatively answers the question below Theorem 4 in [1] due to L. Catalano.