Certain functional identities on division rings of characteristic two
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916276696252416 |
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| author | Eroğlu, Münevver Pınar Lee, Tsiu-Kwen Lin, Jheng-Huei |
| author_facet | Eroğlu, Münevver Pınar Lee, Tsiu-Kwen Lin, Jheng-Huei |
| contents | 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 $\text{char}\, D=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13650 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Certain functional identities on division rings of characteristic two Eroğlu, Münevver Pınar Lee, Tsiu-Kwen Lin, Jheng-Huei Rings and Algebras 16R60 (Primary) 16R50, 16K40 (Secondary) 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 $\text{char}\, D=2$. |
| title | Certain functional identities on division rings of characteristic two |
| topic | Rings and Algebras 16R60 (Primary) 16R50, 16K40 (Secondary) |
| url | https://arxiv.org/abs/2403.13650 |