- Tytuł:
- Additive mappings satisfying algebraic identities in semiprime rings
- Autorzy:
- Ansari, Abu Zaid
- Tematy:
-
semiprime rings
generalized $(\alpha
\beta)$-derivation
generalized left $(\alpha
\beta)$-derivation and additive mappings - Pokaż więcej
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Powiązania:
- https://bibliotekanauki.pl/articles/59445231.pdf Link otwiera się w nowym oknie
- Opis:
- Let $R$ be a $k$-torsion free semiprime ring. Suppose that $F, d : R\to R$ be two additive mappings which satisfy the algebraic identity $F(x^{2n})=F(x^n) \alpha(x^n)+ \beta(x^n) d(x^n)$ for all $x\in R$, where $\alpha$ and $\beta$ are automorphisms on $R$. Then $F$ is a generalized $(\alpha,\beta)$-derivation with associated $(\alpha,\beta)$-derivation $d$ on $R$, where $k\in\{2,n,2n-1\}$. On the other hand, it is proved that $f$ is a generalized Jordan left $(\alpha, \beta)$-derivation associated with Jordan left $(\alpha, \beta)$-derivation $\delta$ on $R$ if they satisfy the algebraic identity $f(x^{2n})=\alpha(x^n) f(x^n)+ \beta(x^n)\delta(x^n)$ for all $x\in R$ together with some restrictions on $R$.
- Dostawca treści:
- Biblioteka Nauki
Artykuł