Multiplicative generalized derivations on ideals in semiprime rings

Rok, strany: 2016, 1285 - 1296

Let $R$ be a ring and $I$ is a nonzero ideal of $R$. A mapping $F:R\rightarrow R$ is called a multiplicative generalized derivation if there exists a mapping $g:R\rightarrow R$ such that $F(xy)=F(x)y+xg(y)$, for all $x,y\in R$. In the present paper, we shall prove that $R$ contains a nonzero central ideal if any one of the following holds: i) $F([x,y])=0$, vii) $F([x,y])=\pm\lbrack F(x),y]$, ii) $F(xoy)=0$, viii) $F(xoy)=\pm(F(x)oy)$, iii) $F([x,y])=\pm\lbrack x,y]$, ix) $F(xy)\pm xy\in Z$, iv) $F(xoy)=\pm(xoy)$, x) $F(xy)\pm yx\in Z$, v) $F([x,y])=\pm(xoy)$, xi) $F(xy)\pm\lbrack x,y]\in Z$, vi) $F(xoy)=\pm\lbrack x,y]$, xii) $F(xy)\pm(xoy)\in Z$, for all $x,y\in I$.

ISO 690:

Gölbaşi, Ö. 2016. Multiplicative generalized derivations on ideals in semiprime rings. In Mathematica Slovaca, vol. 66, no.6, pp. 1285-1296. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0223

APA:

Gölbaşi, Ö. (2016). Multiplicative generalized derivations on ideals in semiprime rings. Mathematica Slovaca, 66(6), 1285-1296. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0223