Certain functional identities on division rings of characteristic two
JOURNAL OF ALGEBRA, cilt.0, sa.0, ss.1-14, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 0 Sayı: 0
- Basım Tarihi: 2024
- Doi Numarası: 10.1016/j.jalgebra.2024.05.022
- Dergi Adı: JOURNAL OF ALGEBRA
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
- Sayfa Sayıları: ss.1-14
- Anahtar Kelimeler: Division ring, Additive map, Elementary operator, Hua's identity, Functional identity, PI-algebra, GPI-algebra
- Dokuz Eylül Üniversitesi Adresli: Evet
Özet
Let $D$ be a noncommutative division ring. In a recent paper, Lee and Lin proved that if $\text{char}\, D\ne 2$, the only solution of additive maps $f, g$ on $D$ satisfying the identity $f(x) = x^n g(x^{-1})$ on $D\setminus \{0\}$ with $n\ne 2$ a positive integer is the trivial case, that is, $f=0$ and $g=0$. Applying Hua's identity and the theory of functional and generalized polynomial identities, we give a complete solution of the same identity for any nonnegative integer $n$ if $\text{char}\, D=2$.