Let $R$ be an associative ring. An additive map $F:R\toR$ is called a generalized derivation if there exists a derivation $d$ of $R$ such that $F(xy)=F(x)y+xd(y)$ for all $x,y\in R$. In [7], Herstein proved the following result: If $R$ is a prime ring of $char(R)\neq 2$ admitting a nonzero derivation $d$ such that $[d(x),d(y)]=0$ for all $x,y\in R$, then $R$ is commutative. In the present paper, we shall study the above mentioned result for generalized derivations in rings with involution.
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Yayımlanma Tarihi | 1 Aralık 2017 |
Yayımlandığı Sayı | Yıl 2017 Cilt: 46 Sayı: 6 |